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We study the first‐order stochastic dominance (SD) test in the context of two independent random samples. We introduce several test statistics that effectively capture violations of the dominance relationship, particularly in the tail regions. Additionally, we develop a resampling procedure to compute the p‐values or critical values for these tests. The proposed tests have asymptotic type I error rates for frontal configurations equal to the nominal level α. Furthermore, their powers approach 1 for any fixed alternatives. Through simulation experiments, we demonstrate that our SD tests outperform the recentring test proposed by Donald and Hsu (2016) as well as the integral‐type test presented by Linton et al. (2010) in various scenarios discussed in existing literature. We also employ the proposed tests to analyze changes in the distribution of household income in the United Kingdom over time. The proposed tests offer some insights into potential dominance relationships within this context. [ABSTRACT FROM AUTHOR]

For the KPZ equation on a torus with a 1 + 1 spacetime white noise, it was shown in Dunlap et al. (Commun Pure Appl Math, 2023, https://doi.org/10.1002/cpa.22110) and Gu and Komorowski (Ann Inst H Poincare Prob Stat, 2021, arXiv:2104.13540v2) that the height function satisfies a central limit theorem, and the variance can be written as the expectation of an exponential functional of Brownian bridges. In this paper, we consider another physically relevant quantity, the winding number of the directed polymer on a cylinder, or equivalently, the displacement of the directed polymer endpoint in a spatially periodic random environment. It was shown in Gu and Komorowski (SIAM J Math Anal, arXiv:2207.14091) that the polymer endpoint satisfies a central limit theorem on diffusive scales. The main result of this paper is an explicit expression of the effective diffusivity, in terms of the expectation of another exponential functional of Brownian bridges. Our argument is based on a combination of tools from Malliavin calculus, homogenization, and diffusion in distribution-valued random environments. [ABSTRACT FROM AUTHOR]

Background: Animal habitat use can be influenced by a suite of factors including intraspecific interactions and resource availability. The broad-snouted caiman (Caiman latirostris) is the largest crocodylian species distributed in freshwater environments of the Brazilian Atlantic Forest, where it inhabits many types of human-impacted and preserved habitats. Despite their ability to occupy ecologically different water bodies, little is known about their movement patterns and their habitat use. We investigated the variation in movements and space use of adult caimans relative to sex, body condition, and environmental conditions in northeastern Brazil. Methods: We conducted long-term capture surveys from 2013 to 2022 and used GPS telemetry from 2021–2022 (n = 12 individuals) to assess movement patterns and home ranges of caimans and their habitat use based on Brownian Bridge Movement Modeling (BBMM) and Generalized Linear Mixed Modeling (GLMM). Results: Females ranged farther from reservoir's forested margins, exploring a greater diversity of habitats during the wet/non-reproductive season. During the dry/reproductive season, females remained close to nesting sites within forest fragments. The body condition of caimans did not change significantly over the wet and dry season, indicating that resources are available year-round. Caimans moved more at night than during daytime, likely due to nocturnal foraging and possibly avoiding periods of increased human activity. Female movement rates were positively associated with rainfall, in a pattern likely linked to nest attendance in the dry season. Male movement was positively correlated with reservoir volume in the wet season, possibly due to increased availability of habitats in comparison to dry periods and to decreased overlap with territories controlled by other males. Home ranges estimated as 95% utilization distributions were relatively small in both sexes, averaging 0.64 km2 (range: 0.001–1.4 km2), as were their core areas estimated as 50% utilization distributions, which averaged 0.12 km2 (range: 0.0003–0.12 km2). Small core areas may indicate that caimans remain most of their time in a specific habitat, suggesting abundant resource availability or territoriality. Conclusions: Our work reveals the complexity of social interactions and how caimans select their habitats in a highly altered environment. [ABSTRACT FROM AUTHOR]

By changing the spatiotemporal availability of resources, tourism-related feeding can have potentially detrimental impacts on the movement ecology of animals, thus possibly undermining its own conservation benefits. A lack of baseline data on natural behaviour and the noninclusion of observation data that adequately incorporates the previous experience of animals with tourism-related feeding have generated contradictory results, causing the true impacts of feeding to remain obscure. Further, the relationship between the energy consumption of fed animals and their space use remains unexplored. Here, we coupled passive acoustic telemetry with previously published observation data at a tourism-related feeding site to investigate how direct feeding affects space use and residency patterns of great hammerhead sharks, Sphyrna mokarran , in Bimini, The Bahamas, at various timescales (ranging from days to 8 years). We first constructed movement models for 28 known fed and naïve sharks (i.e. those that were present at the study site but never attended feeding events) to quantify differences in space use and spatial overlap between those groups. We then compared bait uptake of fed sharks with their space use. Fed sharks showed a marked reduction in space use in response to feeding events and an amplification of these impacts over 5 consecutive years. In contrast, naïve shark space use remained unchanged over the same period. The seasonal residency of fed and naïve great hammerheads remained stable across 8 years, with the sharks leaving the study site during the summer of each year. Our study underscores how the intensification of tourism-related direct feeding progressively alters the space use of apex predators across short and long timescales, with enduring effects on fed animals. Our study further highlights the utility of a naïve animal group for assessing feeding impacts in the absence of baseline data. • Tourism-related feeding reduced short-term local space use of fed sharks. • Long-term amplification of these impacts occurred across 5 years in fed sharks. • Reduction in local space use of fed sharks was independent of bait consumption. • Local space use of naïve sharks was not impacted by tourism-related feeding. • Feeding site residency indices of fed and naïve sharks were stable across 8 years. [ABSTRACT FROM AUTHOR]

To access seals (Pinnipedia), polar bears (Ursus maritimus) move large distances over the sea ice in winter. Already documented declines in ice duration for Hudson Bay, Canada, are predicted to continue, likely affecting polar bear movement patterns. Using data from global positioning system (GPS) collars, 2007–2011, we describe movement patterns of adult female polar bears of the Southern Hudson Bay (SH) subpopulation. We tested effects of season and reproductive class on movement rates, distance travelled, displacement distance and direction, and home range size. Except for denning females, reproductive class had no effect on movement rates, which were greatest during freeze-up and least during summer. Across all reproductive classes and seasons, mean hourly movement rate was 0.63 km/hour. Mean annual distance moved by nondenning females was 4,771 km. During freeze-up, bears moved north-easterly from the Ontario coast toward the Belcher Islands and Québec following the forming ice edge. During breakup, bears moved southerly toward the Ontario coast and away from the residual ice that occurs north of the Ontario coast. In autumn, denning females moved southerly and inland to den. Mean annual minimum convex polygon (MCP) home-range size was 153,866 km2, with no effect of reproductive class nor change over time. Home range estimates from kernel density estimators and Brownian bridge movement models (BBMM) varied by reproductive class and were smaller than MCP ones. The BBMM estimates likely yield more realistic patterns of space use by polar bears. Using data from satellite collars, 1997–2003, we compared travel distance and home range size between periods (1997–2003; 2007–2011). We found weak evidence of a difference in distance moved between periods, perhaps due to a period of ice stability in the 2000s. Our results identified patterns of use of extensive areas of Hudson Bay by SH bears in winter, and results provide benchmarks for future studies of movement patterns. [ABSTRACT FROM AUTHOR]

This paper delves into the asymptotic theory of a Cumulative Sum (CUSUM)-type test designed for detecting change points in the variance of AutoRegressive Moving-Average models, incorporating Generalized Autoregressive Conditional Heteroscedasticity innovations. We demonstrate that, under the null hypothesis (no change), the CUSUM test statistic converges to the supremum of a standard Brownian bridge. Using a Monte Carlo simulation, we highlight the strong performance of our proposed test when compared to the methods by Song and Kang. Furthermore, we provide a real-world data analysis to showcase the practical application of our test. [ABSTRACT FROM AUTHOR]

Woodland caribou (Rangifer tarandus caribou) are designated as Threatened or Endangered in Canada, with many populations being at risk of extirpation. Approaches for caribou conservation can be both invasive and expensive. For example, maternity penning involves the relocation of pregnant females to a predator‐free fenced enclosure where they are held for 20–22 weeks. This activity greatly reduces the risk of predation for adult females and their dependent calves, but requires the construction, maintenance, and monitoring of a penning facility as well as the risk associated with the capture and transport of adult caribou. With only four maternity pen trials within the last decade, there has been little study of the potential influence of maternity penning on the distribution and habitat use of caribou after release. We used Brownian Bridge Movement Models to examine changes in range fidelity and overall range use of the Klinse‐Za caribou herd in north‐central British Columbia, Canada, following eight years of maternity penning. We generated annual home range utilisation distributions and examined the space use of caribou among years and between penned and unpenned animals, as well as pre‐penning and post‐penning time periods. We found that following penning, caribou shifted distribution to areas near maternity pens and expanded their overall use of range. However, caribou did not shift their distribution relative to the elevation of their mountainous habitats. Our results suggest that caribou can adapt to capture and forced displacement without altering patterns of instinctual or learned habitat use. [ABSTRACT FROM AUTHOR]

Migration is an integral part of the annual cycle of many bird species that have evolved to take advantage of spatially segregated, seasonally abundant food resources while avoiding harsh winter conditions. Increasing evidence suggests that long-distance migrants are shortening their migration routes and wintering at higher latitudes closer to their breeding grounds. One potential example of this process are the observations of Egyptian vultures during the winter on the island of Crete. In this study we provide an overview of wintering Egyptian vulture occurrences on the island of Crete, seeking to shed additional light on the species’ wintering ecology. To this aim we collated extensive field observations spanning 28 winters from 1995 to 2023 and analysed telemetry data from three tracked vultures. Our results revealed a change in the wintering frequency of Egyptian vultures in the island with an increasing trend since 2015, especially regarding the presence of subadult and adult birds. We found an increased habitat use intensity for open landscapes and agricultural areas compared to other habitat types within Crete, emphasizing the influence of food availability on space utilization. We suggest that the interplay between climate changes, lack of experienced conspecifics and local food availability could have triggered the increasing number of wintering Egyptian vultures in Crete. The implications of this short-stopping behaviour extend to conservation strategies, highlighting the need for the consideration of new wintering sites and the potential threats faced by vultures during this period. We recommend the operation of supplementary feeding stations and actions to reduce the risk of electrocution to be considered as valuable conservation actions in the species’ wintering sites in Crete. Monitoring and further research are recommended to assess the long-term impact and viability of this new migration tactic, providing insights into adaptive responses to environmental change. [ABSTRACT FROM AUTHOR]

Acoustic telemetry is a common tool used in fisheries management to estimate fish space use (i.e., occupancy) from a local habitat scale to entire systems. Numerous analytical models have been developed to estimate different aspects of fish movement from telemetry datasets, yet evaluations of model performance and comparisons among models are limited. Here, we develop a framework to evaluate model estimates of regional occupancy in large and fragmented systems using an acoustic receiver array in Lake Champlain. We simulated the tracks of 100 acoustically tagged fish using a random walk function and created detection events based on receiver positions and distance-based detection probability. Regional occupancy for the simulated data was estimated by six movement models that ranged in analytical complexity, and results were compared to the true distributions for each simulated track to evaluate model error. The six movement models included: (1) a basic residency index using detections alone; (2) a residency index using last-observation-carried-forward; (3) a centers of activity model; (4) linear and non-linear interpolations (i.e., least-cost paths); and (5 and 6) two dynamic Brownian bridge movement models generated using separate packages in R. We developed a model selection process to compare model performance and select the optimal analysis based on simulation error. This process showed significant differences in model performance among the six movement models based on model error. Overall, the model generating least-cost paths using linear and non-linear interpolations consistently provided the most accurate regional occupancy estimates. Based on these simulation results, we applied this model to a case study that evaluated patterns in the regional distribution of stocked lake trout (Salvelinus namaycush) in Lake Champlain, which demonstrated distinct regional occupancy of two stocked lake trout groups. These results demonstrate potential for large variability in interpretation of acoustic telemetry data for describing regional fish distribution dependent on the analytical method used. [ABSTRACT FROM AUTHOR]

We consider testing for trend in recurrent event data. More precisely, for such data we consider testing of the null hypothesis of data coming from a renewal process. The new tests are essentially obtained by considering appropriate integrated versions of classical trend tests. Moreover, adaptive versions of earlier considered tests versus non‐monotonic alternatives, like bathtub trend, are suggested. A simulation study shows that the new tests have favorable properties and sometimes outperform classical tests. Examples with real data are also considered. [ABSTRACT FROM AUTHOR]

Many ungulates migrate between distinct summer and winter ranges, and identifying, mapping, and conserving these migration corridors have become a focus of local, regional, and global conservation efforts. Brownian bridge movement models (BBMMs) are commonly used to empirically identify these seasonal migration corridors; however, they require location data sampled at relatively frequent intervals to obtain a robust estimate of an animal's movement path. Fitting BBMMs to sparse location data violates the assumption of conditional random movement between successive locations, overestimating the area (and width) of a migration corridor when creating individual and population‐level occurrence distributions and precluding the use of low‐frequency, or sparse, data in mapping migration corridors. In an effort to expand the utility of BBMMs to include sparse GPS data, we propose an alternative approach to model migration corridors from sparse GPS data. We demonstrate this method using GPS data collected every 2 h from four mule deer (Odocoileus hemionus) and four elk (Cervus canadensis) herds within Wyoming and Idaho. First, we used BBMMs to estimate a baseline corridor for the 2‐h data. We then subsampled the 2‐h data to one location every 12 h (a proxy for sparse data) and fitted BBMMs to the 12‐h data using a fixed motion variance (FMV) value, instead of estimating the Brownian motion variance empirically. A range of FMV values was tested to identify the value that best approximated the baseline migration corridor. FMV values within a species‐specific range (mule deer: 400–1200 m2; elk: 600–1600 m2) successfully delineated migration corridors similar to the 2‐h baseline corridors; overall, lower values delineated narrower corridors and higher values delineated wider corridors. Optimal FMV values of 800 m2 (mule deer) and 1000 m2 (elk) decreased the inflation of the 12‐h corridors relative to the 2‐h corridors from traditional BBMMs. This FMV approach thus enables using sparse movement data to approximate realistic migration corridor dimensions, providing an important alternative when movement data are collected infrequently. This approach greatly expands the number of datasets that can be used for migration corridor mapping—a useful tool for management and conservation across the globe. [ABSTRACT FROM AUTHOR]

We present a new quadratic Gaussian short rate model with a stochastic lower bound to capture changes in the yield curve including negative interest rates, associated with changes in monetary policy stances. We model the lower bound by a Brownian bridge pinned at zero at the initial time and at a random termination time, representing the first appearance of negative interest rates and the end date of an unconventional monetary policy, respectively. Within this framework, we derive a semi-analytical pricing formula for zero coupon bonds under the no-arbitrage condition. Our model estimation results using Japanese yield curve data show a good fit to the market data. Furthermore, the expected excess bond returns and the posterior distribution of the unconventional monetary policy duration computed from the model parameter and state variable estimates clarify the market's perspective on monetary policy developments. [ABSTRACT FROM AUTHOR]

Moderate calibration, the expected event probability among observations with predicted probability z being equal to z, is a desired property of risk prediction models. Current graphical and numerical techniques for evaluating moderate calibration of risk prediction models are mostly based on smoothing or grouping the data. As well, there is no widely accepted inferential method for the null hypothesis that a model is moderately calibrated. In this work, we discuss recently‐developed, and propose novel, methods for the assessment of moderate calibration for binary responses. The methods are based on the limiting distributions of functions of standardized partial sums of prediction errors converging to the corresponding laws of Brownian motion. The novel method relies on well‐known properties of the Brownian bridge which enables joint inference on mean and moderate calibration, leading to a unified "bridge" test for detecting miscalibration. Simulation studies indicate that the bridge test is more powerful, often substantially, than the alternative test. As a case study we consider a prediction model for short‐term mortality after a heart attack, where we provide suggestions on graphical presentation and the interpretation of results. Moderate calibration can be assessed without requiring arbitrary grouping of data or using methods that require tuning of parameters. [ABSTRACT FROM AUTHOR]

Home range and home range overlap can be used to describe use of space and movement of wildlife. During the last years, advancements in technology have greatly improved our understanding of animal movement, especially among large herbivores. Wild ungulate abundance and distribution have increased in temperate areas. Moreover, their diseases—including sarcoptic mange in the Iberian Ibex (Capra pyrenaica)—have become a cause of concern for livestock, public health, and wildlife conservation. In this study, we first reviewed existing literature on the home range of species in the genus Capra. We then analyzed data from 52 GPS-GSM-collared Iberian ibexes, of which 33 were healthy and 19 were affected by sarcoptic mange from 3 different populations in the southeastern Iberian Peninsula to analyze: (1) differences in size and characteristics of home ranges obtained by the 3 most commonly used methodologies—minimum convex polygon, kernel density estimation, and Brownian bridges movement models (BBMMs); and (2) the impact of endemic sarcoptic mange on Iberian Ibex home range. The literature review revealed that available information on spatial behavior of Capra spp. was based only on 3 species, including the Iberian Ibex, estimated through a diversity of methods which made it difficult to compare results. We found positive correlations among the different home range estimation methods in the Iberian Ibex, with BBMMs proving to be the most accurate. This study is the first to use BBMMs for estimating home range in this species, and it revealed a marked seasonal behavior in spatial use, although sarcoptic mange smoothed such seasonal pattern. The seasonal overlaps obtained suggest that core areas of the Iberian Ibex change within wider home range areas, which are ecological parameters relevant to identifying key areas for species management and conservation. [ABSTRACT FROM AUTHOR]

The Brownian bridge or Lévy–Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. We focus on the uniform error. In particular, we show constructively that at level N , at which there are $d=2^N$ points evaluated on the Brownian path, the uniform error and its square, and the uniform error of geometric Brownian motion, have upper bounds of order $\mathcal {O}(\sqrt {\ln d/d})$ , matching the known orders. We apply the results to an option pricing example. [ABSTRACT FROM AUTHOR]

We give the Karhunen–Loève expansion of the covariance function of a family of discrete weighted Brownian bridges, appearing as discrete analogues of continuous Gaussian processes related to Cramér –von Mises and Anderson–Darling statistics. This analogy enables us to introduce a discrete Cramér–von Mises statistic and show that this statistic satisfies a property of local asymptotic Bahadur optimality for a statistical test involving the classical hypergeometric distributions. Our statistic and the goodness-of-fit problem we deal with are based on basic properties of Hahn polynomials and are, therefore, subject to some extension to all families of classical orthogonal polynomials, as well as their q-analogues. Due probably to computational difficulties, the family of discrete Cramér–von Mises statistics has received less attention than its continuous counterpart—the aim of this article is to bridge part of this gap. [ABSTRACT FROM AUTHOR]

It may happen that the behavior of a multivariate time series is such that the underlying joint distribution is gradually moving from one distribution to another between unknown times of change. Under this context of a possible gradual-change, tests of change-point detection in the dependence structure of multivariate series are developed around the associated sequence of Spearman matrices. It is formally established that the proposed test statistics for that purpose are asymptotically marginal-free under a general strong-mixing assumption, and written as functions of integrated Brownian bridges. Consistent estimators of the pair of times of change, as well as of the before-the-change and after-the-change Spearman matrices, are also proposed. A simulation study examines the sampling properties of the introduced tools, and the methodologies are illustrated on a synthetic dataset. [ABSTRACT FROM AUTHOR]

Suppose that a sequence of random pairs (X 1 , Y 1) , ... , (X n , Y n) is subject to a gradual change in the sense that for K 1 ≤ K 2 ∈ { 1 , ... , n } , the joint distribution is F before K 1 , G after K 2 , and gradually moving from F to G between the two times of change K 1 and K 2 . This setup elegantly generalizes the abrupt-change model that is usually assumed in the change-point analysis. Under this configuration, asymptotically unbiased estimates of Kendall's tau up to and after the change are proposed, as well as tests and estimators of change points related to these measures. The asymptotic behaviour of the introduced estimators and test statistics is rigorously investigated, in particular by demonstrating a general result on weighted indexed U-statistics computed under a heterogeneous pattern. A simulation study is conducted to examine the sampling properties of the proposed methods under different scenarios of change in the dependence structure of bivariate series. An illustration is given on a time series of monthly atmospheric carbon dioxide concentrations and global temperature for the period 1959–2015. [ABSTRACT FROM AUTHOR]

Mojave desert tortoise (Gopherus agassizii) populations in some regions have declined by >50% since 2004, prompting the need for more research on ways to recover populations. One possible recovery tool is head‐starting (i.e., the act of protecting and raising juvenile tortoises to sizes that increase survival upon release); however, head‐starting can have high start‐up and maintenance costs that can limit its feasibility. Strategies that reduce cost and rearing duration may foster broader and more effective use. We released and radio‐tracked 60 juvenile tortoises in the Mojave National Preserve in California, USA, that had been reared under 2 treatments: those reared 1 year indoors after hatching, then 1 year outdoors (combo) and those reared just 1 year indoors (indoor‐only). We tested whether indoor‐only rearing alone could be a more efficient means of producing robust head‐started tortoises. We examined the behavior, movement, and survival of tortoises after release into the wild from 2020 to 2021 to determine whether these outcomes differed between husbandry treatments. Combo tortoises tended to perform settling behaviors (mean ± 1 SE days to building first burrow = 6.7 ± 0.8, entering dormancy = 23.3 ± 2.1, and emerging from dormancy = 189.6 ± 4.4) earlier than indoor‐only tortoises (7.4 ± 0.9, 31.5 ± 2.6, and 193.9 ± 5.9, respectively), but this difference was not significant, suggesting the rearing method did not greatly alter settling behavior. Indoor‐only tortoises dispersed at least twice as far from their release site (156.2 ± 26.3 m compared with 77.3 ± 20.6 m for combo tortoises), had larger mean use areas (3.7 ± 0.1 ha compared with 2.8 ± 0.3 ha for combo tortoises for 95% Brownian bridge movement model estimates), and greater variability in their movements than combo tortoises (daily average step length post‐emergence: 4.3 ± 0.2 m compared with 2.8 ± 0.1 m for combo tortoises). Despite differences in their movements, indoor‐only and combo tortoises had similar survival rates over the study, 51% versus 42%, respectively, during a period of extreme drought in 2021. The similarity in survival between groups gives head‐starting practitioners freedom in their rearing methods. The indoor‐only group had lower site fidelity, which should be considered when this is an undesirable trait for released tortoises. [ABSTRACT FROM AUTHOR]

We consider a pair of traders in a market where the information available to the second trader is a strict subset of the information available to the first trader. The traders make prices based on information concerning a security that pays a random cash flow at a fixed time T in the future. Market information is modeled in line with the scheme of Brody, Hughston, and Macrina. The risk-neutral distribution of the cash flow is known to the traders, who make prices with a fixed multiplicative bid-offer spread and report their prices to a game master who declares that a trade has been made when the bid price of one of the traders crosses the offer price of the other. We prove that the value of the first trader's position is strictly greater than that of the second. The results are analyzed by use of simulation studies and generalized to situations where (a) there is a hierarchy of traders, (b) there are multiple successive trades, and (c) there is inventory aversion. In these settings, we show that information is superior to strategy. [ABSTRACT FROM AUTHOR]

We develop a fast Monte Carlo simulation (MCS) for pricing equity-linked securities (ELS) with time-dependent volatility and interest rate. In this paper, we extend a recently developed fast MCS for pricing ELS. In the previous model, both the volatility and interest rate were constant. However, in the real finance market, volatility and interest rate are time-dependent parameters. In this work, we approximate the time-dependent parameters by piecewise constant functions and apply Brownian bridge technique. We present some numerical results of the proposed method. The computational results demonstrate the fastness of the proposed algorithm with equivalent accuracy with standard MCS. It is important for traders and hedgers considering derivatives to evaluate prices and risks quickly and accurately. Therefore, our algorithm will be very useful to practitioners in the ELS market. [ABSTRACT FROM AUTHOR]

Background: Prey are more vulnerable during migration due to decreased familiarity with their surroundings and spatially concentrated movements. Predators may respond to increased prey vulnerability by shifting their ranges to match prey. Moose (Alces alces) and white-tailed deer (Odocoileus virginianus) are primary gray wolf (Canis lupus) prey and important subsistence species for Indigenous communities. We hypothesized wolves would increase use of ungulate migration corridors during migrations and predicted wolf distributions would overlap primary available prey. Methods: We examined seasonal gray wolf, moose, and white-tailed deer movements on and near the Grand Portage Indian Reservation, Minnesota, USA. We analyzed GPS collar data during 2012–2021 using Brownian bridge movement models (BBMM) in Migration Mapper and mechanistic range shift analysis (MRSA) to estimate individual- and population-level occurrence distributions and determine the status and timing of range shifts. We estimated proportional overlap of wolf distributions with moose and deer distributions and tested for differences among seasons, prey populations, and wolf sex and pack affiliations. Results: We identified a single migration corridor through which white-tailed deer synchronously departed in April and returned in October–November. Gray wolf distributions overlapped the deer migration corridor similarly year-round, but wolves altered within-range distributions seasonally corresponding to prey distributions. Seasonal wolf distributions had the greatest overlap with deer during fall migration (10 October–28 November) and greatest overlap with moose during summer (3 May–9 October). Conclusions: Gray wolves did not increase their use of the white-tailed deer migration corridor but altered distributions within their territories in response to seasonal prey distributions. Greater overlap of wolves and white-tailed deer in fall may be due to greater predation success facilitated by asynchronous deer migration movements. Greater summer overlap between wolves and moose may be linked to moose calf vulnerability, American beaver (Castor canadensis) co-occurrence, and reduced deer abundance associated with migration. Our results suggest increases in predation pressure on deer in fall and moose in summer, which can inform Indigenous conservation efforts. We observed seasonal plasticity of wolf distributions suggestive of prey switching; that wolves did not exhibit migratory coupling was likely due to spatial constraints resulting from territoriality. [ABSTRACT FROM AUTHOR]

We introduce a new class of stochastic processes called fractional Wiener–Weierstraß bridges. They arise by applying the convolution from the construction of the classical, fractal Weierstraß functions to an underlying fractional Brownian bridge. By analyzing the p-th variation of the fractional Wiener–Weierstraß bridge along the sequence of b-adic partitions, we identify two regimes in which the processes exhibit distinct sample path properties. We also analyze the critical case between those two regimes for Wiener–Weierstraß bridges that are based on a standard Brownian bridge. We furthermore prove that fractional Wiener–Weierstraß bridges are never semimartingales, and we show that their covariance functions are typically fractal functions. Some of our results are extended to Weierstraß bridges based on bridges derived from a general continuous Gaussian martingale. [ABSTRACT FROM AUTHOR]

We present a new method to sample conditioned trajectories of a system evolving under Langevin dynamics based on Brownian bridges. The trajectories are conditioned to end at a certain point (or in a certain region) in space. The bridge equations can be recast exactly in the form of a non-linear stochastic integro-differential equation. This equation can be very well approximated when the trajectories are closely bundled together in space, i.e., at low temperature, or for transition paths. The approximate equation can be solved iteratively using a fixed point method. We discuss how to choose the initial trajectories and show some examples of the performance of this method on some simple problems. This method allows us to generate conditioned trajectories with a high accuracy. [ABSTRACT FROM AUTHOR]

A Brownian bridge is a continuous random walk conditioned to end in a given region by adding an effective drift to guide paths toward the desired region of phase space. This idea has many applications in chemical science where one wants to control the endpoint of a stochastic process—e.g., polymer physics, chemical reaction pathways, heat/mass transfer, and Brownian dynamics simulations. Despite its broad applicability, the biggest limitation of the Brownian bridge technique is that it is often difficult to determine the effective drift as it comes from a solution of a Backward Fokker–Planck (BFP) equation that is infeasible to compute for complex or high-dimensional systems. This paper introduces a fast approximation method to generate a Brownian bridge process without solving the BFP equation explicitly. Specifically, this paper uses the asymptotic properties of the BFP equation to generate an approximate drift and determine ways to correct (i.e., re-weight) any errors incurred from this approximation. Because such a procedure avoids the solution of the BFP equation, we show that it drastically accelerates the generation of conditioned random walks. We also show that this approach offers reasonable improvement compared to other sampling approaches using simple bias potentials. [ABSTRACT FROM AUTHOR]

The Natura 2000 network of protected areas is the backbone of species conservation in the European Union. We investigated whether Austrian-hatched white-tailed eagles (Haliaeetus albicilla) make particular use of this multinational network during their natal dispersal, and what habitats were of importance to the eagles. We analyzed the utilization distribution of 907,466 GPS locations from 38 dispersing white-tailed eagles using a dynamic Brownian Bridge Movement Model. Eagles ranged over a huge area of central-eastern Europe. Natura 2000 sites overlapped with 67% of the resulting 50% isopleth; i.e., a high probability of utilization of Natura 2000 areas by white-tailed eagles was found. White-tailed eagles used wetlands, waterbodies, and deciduous forests adjacent to wet habitats disproportionately often. Coniferous forests and settlements were avoided. Anthropogenically caused mortalities hardly occurred within Natura 2000 sites. Our study suggests that the Natura 2000 network is a crucial tool for conserving the white-tailed eagle. This top predator is an ambassador for the Natura 2000 idea during all life stages, and should continue to be a conservation priority of the network. [ABSTRACT FROM AUTHOR]

Multiple sensors are commonly used for accelerated degradation monitoring. Since different sensors may be sensitive at different stages of the accelerated degradation process and each sensor dataset may contain only partial information of the unit degradation, then integration approaches of the accelerated degradation data from multiple sensors can effectively improve degradation modeling and life prediction accuracy. We present a non‐parametric approach that assigns weights to each sensor based on the dynamic clustering of the sensors' observations. Missing data are common in degradation data acquisition, especially when multiple sensors are used. We provide two approaches for data interpolation: the nonlinear Brownian bridge and the inverse Gaussian bridge when the underlying degradation paths follow the Brownian motion process and inverse Gaussian process, respectively. The stochastic bridges capture the nonlinearity and uncertainties of the degradation processes. The data integration model and stochastic bridge models are validated with real accelerated fatigue crack growth data monitored with multiple NDT sensors. The proposed models provide an accurate accelerated degradation path and reliability prediction. [ABSTRACT FROM AUTHOR]

The epistemic arrow of time is the fact that our knowledge of the past seems to be both of a different kind and more detailed than our knowledge of the future. Just like with the other arrows of time, it has often been speculated that the epistemic arrow arises due to the second law of thermodynamics. In this paper, we investigate the epistemic arrow of time using a fully formal framework. We begin by defining a memory system as any physical system whose present state can provide information about the state of the external world at some time other than the present. We then identify two types of memory systems in our universe, along with an important special case of the first type, which we distinguish as a third type of memory system. We show that two of these types of memory systems are time-symmetric, able to provide knowledge about both the past and the future. However, the third type of memory systems exploits the second law of thermodynamics, at least in all of its instances in our universe that we are aware of. The result is that in our universe, this type of memory system only ever provides information about the past. We also argue that human memory is of this third type, completing the argument. We end by scrutinizing the basis of the second law itself. This uncovers a previously unappreciated formal problem for common arguments that try to derive the second law from the "Past Hypothesis", i.e., from the claim that the very early universe was in a state of extremely low entropy. Our analysis is indebted to prior work by one of us but expands and improves upon this work in several respects. [ABSTRACT FROM AUTHOR]

Introduction of invasive alien species (IAS) is one of the main threats to biodiversity. The Northern raccoon (Procyon lotor), here after named "raccoon," recently introduced and rapidly expanding in three main populations in France, is one of the 47 IAS of concern in the European Union. At this date, there is no study on the ecology of the raccoon in France, yet the acquisition of knowledge of the species in its new environment is an essential step for a better evaluation of its impacts and improving its management. We studied space use and habitat selection by French raccoons in a rural population in the Marne department and in a suburban population in Gironde department, respectively, by tracking 14 individuals with GPS collars between May 2019 and August 2021. We estimated the home ranges' size using minimum convex polygon (MCP), adaptative local convex hull (a-LoCoH), and dynamic Brownian bridge motion model (dBBMM). Habitat selection was studied at the second and third order using Ivlev's electivity index and integrated step selection analysis (iSSA) models, respectively. Our results show that raccoons of the rural population have home ranges twice larger than those of the suburban population. Habitats are selected differently according to the population, highlighting the great plasticity of the raccoon. Woodlands are the most used habitats for both populations; however, anthropized areas also appear to be very attractive for the rural population. Surprisingly, this is not the case for the suburban population, which tends to avoid these habitats in favor of the wetland. [ABSTRACT FROM AUTHOR]

Understanding the home range of imperiled reptiles is important to the design of conservation and recovery efforts. Despite numerous home range studies for the Threatened timber rattlesnake (Crotalus horridus), many have limited sample sizes or outdated analytical methods and only a single study has been undertaken in the central midwestern United States. We report on the home range size, site fidelity, and movements of C. horridus in west-central Illinois. Using VHF telemetry, we located 29 C. horridus (13 female, 16 male) over a 5-year period for a total of 51 annual records of the species' locations and movements. We calculated annual home ranges for each snake per year using 99%, 95%, and 50% isopleths derived from Brownian Bridge utilization distributions (BBMM), and we also report 100% minimum convex polygons to be consistent with older studies. We examined the effects of sex, mass, SVL, and year on home range sizes and reported on movement metrics as well as home range fidelity using both Utilization Distribution Overlap Index (UDOI) and Bhattacharyya's affinity (BA) statistics. The home range sizes for male and non-gravid C. horridus were 88.72 Ha (CI 63.41–110.03) and 28.06 Ha (CI 17.17–38.96) for 99% BBMM; 55.65 Ha (CI 39.36–71.93) and 17.98 (CI 10.69–25.28) for 95% BBMM; 7.36 Ha (CI 5.08–9.64) and 2.06 Ha (CI 1.26–2.87) for 50% BBMM; and 78.54Ha (CI 47.78–109.30) and 27.96 Ha (CI 7.41–48.51) for MCP. The estimated daily distance traveled was significantly greater for males (mean = 57.25 m/day, CI 49.06–65.43) than females (mean = 27.55 m/day, CI 18.99–36.12), particularly during the summer mating season. Similarly, maximum displacement distances (i.e., maximum straight-line distance) from hibernacula were significantly greater for males (mean = 2.03 km, CI 1.57–2.48) than females (mean = 1.29 km, CI 0.85–1.73], and on average, males were located further from their hibernacula throughout the entirety of their active season. We calculated fidelity to high-use areas using 11 snakes that were tracked over multiple years. The mean BBMM overlap using Bhattacharyya's affinity (BA) for all snakes at the 99%, 95%, and 50% isopleths was 0.48 (CI 0.40–0.57), 0.40 (0.32–0.49), and 0.07 (0.05–0.10), respectively. The mean BBMM overlap for all snakes using the Utilization Distribution Overlap Index (UDOI) at the 99%, 95%, and 50% isopleths was 0.64 (CI 0.49–0.77), 0.32 (CI 0.21–0.47), and 0.02 (CI 0.01–0.05)), respectively. Our results are largely consistent with those of other studies in terms of the influence of sex on home range size and movements. The species also exhibits strong site fidelity with snakes generally using the same areas each summer, though there is far less overlap in specific (e.g., 50% UDOI) high-use areas, suggesting some plasticity in hunting areas. Particularly interesting was the tendency for snakes to disperse from specific hibernacula in the same general direction to the same general areas. We propose some possible reasons for this dispersal pattern. [ABSTRACT FROM AUTHOR]

A framework for performant Brownian Dynamics (BD) many-body simulations with adaptive timestepping is presented. Contrary to the Euler–Maruyama scheme in common non-adaptive BD, we employ an embedded Heun–Euler integrator for the propagation of the overdamped coupled Langevin equations of motion. This enables the derivation of a local error estimate and the formulation of criteria for the acceptance or rejection of trial steps and for the control of optimal stepsize. Introducing erroneous bias in the random forces is avoided by rejection sampling with memory due to Rackauckas and Nie, which makes use of the Brownian bridge theorem and guarantees the correct generation of a specified random process even when rejecting trial steps. For test cases of Lennard-Jones fluids in bulk and in confinement, it is shown that adaptive BD solves performance and stability issues of conventional BD, already outperforming the latter even in standard situations. We expect this novel computational approach to BD to be especially helpful in long-time simulations of complex systems, e.g., in non-equilibrium, where concurrent slow and fast processes occur. [ABSTRACT FROM AUTHOR]

Schizophrenia is a serious mental disorder, and event-related potentials can effectively reflect the differences between patients and healthy individuals. However, currently, there is no effective method to analyze the Hurst index of short-term electroencephalogram (EEG) signals. This paper improves the calculation method of the Hurst index based on a multipoint fractional Brownian bridge using a genetic algorithm and verifies its feasibility on simulated signals. Through the event-related potential analysis of EEG signals in schizophrenia patients, it was found that the greatest difference between patients and healthy people was in the frontal lobe, and there were differences in the N100 wave, the P50 wave, and the mismatch negativity (MMN) wave in the frontal lobe under sound and action stimulation, and their Hurst index increased. In conclusion, the study found differences in event-related potentials between the frontal and central regions of schizophrenia patients compared to healthy subjects. This research may aid in the diagnosis of schizophrenia patients in clinical practice. [ABSTRACT FROM AUTHOR]

We propose a discrete-time discrete-space Markov chain approximation with a Brownian bridge correction for computing curvilinear boundary crossing probabilities of a general diffusion process on a finite time interval. For broad classes of curvilinear boundaries and diffusion processes, we prove the convergence of the constructed approximations in the form of products of the respective substochastic matrices to the boundary crossing probabilities for the process as the time grid used to construct the Markov chains is getting finer. Numerical results indicate that the convergence rate for the proposed approximation with the Brownian bridge correction is $O(n^{-2})$ in the case of $C^2$ boundaries and a uniform time grid with n steps. [ABSTRACT FROM AUTHOR]

We consider a one-dimensional superprocess with a supercritical local branching mechanism $\psi$ , where particles move as a Brownian motion with drift $-\rho$ and are killed when they reach the origin. It is known that the process survives with positive probability if and only if $\rho , where $\alpha=-\psi'(0)$. When $\rho , Kyprianou et al. [18] proved that $\lim_{t\to \infty}R_t/t =\sqrt{2\alpha}-\rho$ almost surely on the survival set, where $R_t$ is the rightmost position of the support at time t. Motivated by this work, we investigate its large deviation, in other words, the convergence rate of $\mathbb{P}_{\delta_x} (R_t >\gamma t+\theta)$ as $t \to \infty$ , where $\gamma >\sqrt{2 \alpha} -\rho$ , $\theta \ge 0$. As a by-product, a related Yaglom-type conditional limit theorem is obtained. Analogous results for branching Brownian motion can be found in Harris et al. [13]. [ABSTRACT FROM AUTHOR]

Simple Summary: The spiny-tailed lizard Oplurus cyclurus is a widespread endemic iguanian occurring in southern and western Madagascar dry areas. This species is mostly arboreal, and little is known about its spatial ecology. We conducted a radio tracking study on 19 individuals of a population with saxicolous habits, inhabiting an open, treeless savannah in the Isalo sandstone massif (central-southern Madagascar). Tracked lizards had a small home range size (95% isopleth = 247.8 m2) and showed high site and burrow fidelity. The activity pattern was unimodal, increasing along the day and with juveniles more active than adults in unfavourable weather conditions. Basking occurred mostly near the burrow entrance. Despite high burrow fidelity, lizards changed shelters regularly (approx. once a week), but there was no obvious relation between lizards' body and/or tail size and the width and depth of selected burrows. We argue that the saxicolous habits of this population may entail local behavioural adaptations. Understanding the spatial ecology of species has important implications for conservation, as it helps identify suitable habitats and minimum requirements for biodiversity monitoring and management. The spiny-tailed lizard Oplurus cyclurus is a widespread endemic iguanid occurring in dry areas of southern and western Madagascar. While the species is known to be mostly arboreal, populations of the Isalo sandstone massif suggest local adaptation to a less forested savannah and a more exposed habitat. We radio-tracked 19 spiny-tailed lizards to investigate the species' rock-dwelling behaviour and spatial ecology at Isalo National Park. Tracked individuals showed high site and burrow fidelity, and a basking behaviour mostly tied to the accessibility of their burrow, the time of day, and their life stage. Activity peaked during the sunniest hours, while juveniles were more active than adults with unfavourable weather conditions. Despite high burrow fidelity, lizards used shelters non-exclusively, regularly changing (approx. once a week) with neighbouring burrows (average distance between burrows = 13.6 m). However, there was no obvious relation between lizards' body and/or tail size and the width and depth of selected burrows. Dynamic Brownian Bridge Movement Models estimated frequented areas over 247.8 m2 (95% isopleth), where territorial overlap is common. Our results challenge the notion that burrow-site fidelity is the sole driving factor behind space utilization in the studied population. We argue that the apparently unusual saxicolous habits imposed by habitat features (the absence of trees) may lead to local behavioural adjustments influencing antipredatory and foraging strategies, as well as intraspecific interactions. [ABSTRACT FROM AUTHOR]

We revisit the family of goodness-of-fit tests for exponentiality based on the mean residual life time proposed by Baringhaus and Henze [(2008), 'A New Weighted Integral Goodness-of-Fit Statistic for Exponentiality', Statistics & Probability Letters, 78(8), 1006–1016]. We motivate the test statistic by a characterisation of Shanbhag [(1970), 'The Characterizations for Exponential and Geometric Distributions', Journal of the American Statistical Association, 65(331), 1256–1259] and provide an alternative representation, which leads to simple and short proofs for the known theory and an easy to access covariance structure of the limiting Gaussian process under the null hypothesis. Explicit formulas for the eigenvalues and eigenfunctions of the operator associated with the limit covariance are given using results on weighted Brownian bridges. In addition, we derive further asymptotic theory under fixed alternatives as well as approximate Bahadur efficiencies, which provide an insight into the choice of the tuning parameter with regard to the power performance of the tests. [ABSTRACT FROM AUTHOR]

GPS tracking collars were fitted to five free-ranging dogs (Canis familiaris) in the Arcadia Valley, Queensland to establish baseline movement data in this unique topographical landscape. Activity areas were generated with three home range methods using seasonally constrained fixes. Activity areas (Brownian Bridge and Utilisation Distribution) ranged from 2.9 to 689 km2 in this landscape, and revealed that topographical features previously thought to confine free-ranging dog movement were no barrier to habitat use. Free-ranging dogs were collared in the Arcadia valley Queensland to gain insight into how they use the unique topography. Anecdotal evidence suggests that topography like steep cliffs maybe a barrier to home range boundaries; dogs in this short study did not find cliffs a barrier. This information on dog activity helps inform managers on the use of habitat and helps to debunk perceptions around how dogs use the landscape. [ABSTRACT FROM AUTHOR]

In gregarious animals, competition for resources, such as water, food, and shelter, is common. Sleeping sites are one such resource that also may serve strategic functions, such as food or group defense. We investigated whether groups of wild crested macaques (Macaca nigra) compete for sleeping sites and two potential strategic functions of these sites: food defense and group protection. We gathered data from three habituated groups (Pantai Batu 1, Rambo 1, and Rambo 2) in Tangkoko Nature Reserve in North Sulawesi, Indonesia. We collected information on sleeping site use between October 2015 and June 2016, for 192, 156, and 41 nights, for each group respectively. We recorded 229, 207, and 183 travel routes for the three study groups and used these to calculate their home ranges and core areas using Brownian Bridge Movement Models. We also documented 304 intergroup encounters (IGE) among the three habituated groups and their neighbors. We found that suitable sleeping sites for crested macaques are limited, frequently reused, and shared sequentially, but not used simultaneously. There was a strong link between core areas and sleeping site density. However, we found no significant relationship between high IGE risk areas and sleeping site density, nor between core or high IGE risk areas and sleeping site reuse frequency. The study found no correlation between the distance traveled post-encounter to sleeping sites and the encounter's outcome or intensity. Overall, our study adds to the evidence that primates are selective in choosing sleeping sites, whose additional functions might be population specific. [ABSTRACT FROM AUTHOR]

In the present paper, we study the small ball probabilities in L2-norm for a family of finite-dimensional perturbations of Gaussian functions. We define three types of perturbations: noncritical, partially critical and critical; and derive small ball asymptotics for the perturbated process in terms of the small ball asymptotics for the original process. The natural examples of such perturbations appear in statistics in the study of empirical processes with estimated parameters (the so-called Durbin's processes). We show that the Durbin's processes are critical perturbations of the Brownian bridge. Under some additional assumptions, general results can be simplified. As an example, we find the exact L2-small ball asymptotics for critical perturbations of the Green processes (the processes whose covariance function is the Green function of the ordinary differential operator). [ABSTRACT FROM AUTHOR]

This paper studies numerical methods for the approximation of elliptic PDEs with lognormal coefficients of the form -\operatorname {div}(a\nabla u)=f where a=\exp (b) and b is a Gaussian random field. The approximant of the solution u is an n-term polynomial expansion in the scalar Gaussian random variables that parametrize b. We present a general convergence analysis of weighted least-squares approximants for smooth and arbitrarily rough random field, using a suitable random design, for which we prove optimality in the following sense: their convergence rate matches exactly or closely the rate that has been established in Bachmayr, Cohen, DeVore, and Migliorati [ESAIM Math. Model. Numer. Anal. 51 (2017), pp. 341–363] for best n-term approximation by Hermite polynomials, under the same minimial assumptions on the Gaussian random field. This is in contrast with the current state of the art results for the stochastic Galerkin method that suffers the lack of coercivity due to the lognormal nature of the diffusion field. Numerical tests with b as the Brownian bridge confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

Most studies modeling population mobility and the spread of infectious diseases, particularly those using meta-population multi-patch models, tend to focus on the theoretical properties and numerical simulation of such models. As such, there is relatively scant literature focused on numerical fit, inference, and uncertainty quantification of epidemic models with population mobility. In this research, we use three estimation techniques to solve an inverse problem and quantify its uncertainty for a human-mobility-based multi-patch epidemic model using mobile phone sensing data and confirmed COVID-19-positive cases in Hermosillo, Mexico. First, we utilize a Brownian bridge model using mobile phone GPS data to estimate the residence and mobility parameters of the epidemic model. In the second step, we estimate the optimal model epidemiological parameters by deterministically inverting the model using a Darwinian-inspired evolutionary algorithm (EA)—that is, a genetic algorithm (GA). The third part of the analysis involves performing inference and uncertainty quantification in the epidemic model using two Bayesian Monte Carlo sampling methods: t-walk and Hamiltonian Monte Carlo (HMC). The results demonstrate that the estimated model parameters and incidence adequately fit the observed daily COVID-19 incidence in Hermosillo. Moreover, the estimated parameters from the HMC method yield large credible intervals, improving their coverage for the observed and predicted daily incidences. Furthermore, we observe that the use of a multi-patch model with mobility yields improved predictions when compared to a single-patch model. [ABSTRACT FROM AUTHOR]

• A new class of non-stationary binomial AR(1) models with change point. • Parameter estimation with change point known or unknown cases. • Change point testing and forecasting method. • Two real data applications in the field of epidemiology. In this paper, we conduct the statistical inference for a new class of non-stationary binomial AR(1) models with change point. The parameter estimation problem is considered, as well as the testing problem for the possible change point. For this task, a residual-based cumulative sum (CUSUM) test is employed, and we show that the limiting null distributions take the form of the functions of Brownian bridge. In the simulation study, we evaluate the performance of the estimation methods and the respective CUSUM test. We furthermore propose a method for the forecasting of the model. Finally, two real data applications were provided in the field of epidemiology. [ABSTRACT FROM AUTHOR]

The unscaled small-time asymptotics of the density is approached by means of the Brownian bridge, regarding planar analogues of the Langevin diffusion, which are strictly hypoelliptic. While the non-quadratic case remains open, in the quadratic case a new precision is derived. [ABSTRACT FROM AUTHOR]

Spatial linear features are often represented as a series of line segments joined by measured endpoints in surveying and geographic information science. There are not only the measuring errors of the endpoints but also the modeling errors between the line segments and the actual geographical features. This paper presents a Brownian bridge error model for line segments combining both the modeling and measuring errors. First, the Brownian bridge is used to establish the position distribution of the actual geographic feature represented by the line segment. Second' an error propagation model with the constraints of the measuring error distribution of the endpoints is proposed. Third' a comprehensive error band of the line segment is constructed' wherein both the modeling and measuring errors are contained. The proposed error model can be used to evaluate line segments' overall accuracy and trustability influenced by modeling and measuring errors, and provides a comprehensive quality indicator for the geospatial data. [ABSTRACT FROM AUTHOR]

In this paper we study the change point detection for the mean of multivariate time series. We construct the weighted U-statistic change point tests based on the weight function 1 / t (1 - t) and some suitable kernel functions. We establish the asymptotic distribution of the test statistic under the null hypothesis and the consistency under the alternatives. A bootstrap procedure is applied to approximate the distribution of the test statistic and it is proved that the test statistic based on bootstrap sampling has the same asymptotic distribution as the original statistic. Numerical simulation and real data analysis show the good performance of the weighted change point test especially when the change point location is not in the middle of the observation period. [ABSTRACT FROM AUTHOR]

This article derives explicit expressions to simulate theta and gamma for American options using the pathwise derivative method. Although the pathwise derivative formulas for delta, rho, and vega of American options have been studied in the literature, no correct explicit results for theta and gamma exist. In addition, the authors propose a simulation-based least-square method to compute the optimal stopping boundary for American options. The optimal stopping boundary is needed to evaluate our pathwise derivative expression for gamma and can be used in the integral method to calculate the price and Greeks of American options. Their proposed least-square approach to compute the optimal stopping boundary provides an alternative to the traditional recursive method of solving a system of equations. The authors also incorporate a Brownian bridge in the computation of the Greeks and extend the application of their results to American basket options. [ABSTRACT FROM AUTHOR]

We introduce a variant of Shepp's classical urn problem in which the optimal stopper does not know whether sampling from the urn is done with or without replacement. By considering the problem's continuous-time analog, we provide bounds on the value function and, in the case of a balanced urn (with an equal number of each ball type), an explicit solution is found. Surprisingly, the optimal strategy for the balanced urn is the same as in the classical urn problem. However, the expected value upon stopping is lower due to the additional uncertainty present. [ABSTRACT FROM AUTHOR]

We study a multivariate system over a finite lifespan represented by a Hermitian-valued random matrix process whose eigenvalues (i) interact in a mean-field way and (ii) converge to their weighted ensemble average at their terminal time. We prove that such a system is guaranteed to converge in time to the identity matrix that is scaled by a Gaussian random variable whose variance is inversely proportional to the dimension of the matrix. As the size of the system grows asymptotically, the eigenvalues tend to mutually independent diffusions that converge to zero at their terminal time, a Brownian bridge being the archetypal example. Unlike commonly studied random matrices that have non-colliding eigenvalues, the proposed eigenvalues of the given system here may collide. We provide the dynamics of the eigenvalue gap matrix, which is a random skew-symmetric matrix that converges in time to the $\textbf{0}$ matrix. Our framework can be applied in producing mean-field interacting counterparts of stochastic quantum reduction models for which the convergence points are determined with respect to the average state of the entire composite system. [ABSTRACT FROM AUTHOR]

Modelling the growth histories of specific galaxies often involves generating the entire population of objects that arise in a given cosmology and selecting systems with appropriate properties. This approach is highly inefficient when targeting rare systems such as the extremely luminous high-redshift galaxy candidates detected by JWST. Here, we present a novel framework for generating merger trees with branches that are guaranteed to achieve a desired halo mass at a chosen redshift. This method augments extended Press Schechter theory solutions with constrained random processes known as Brownian bridges and is implemented in the open-source semi-analytic model galacticus. We generate ensembles of constrained merger trees to predict the growth histories of seven high-redshift JWST galaxy candidates, finding that these systems most likely merge ≈2 Gyr after the observation epoch and occupy haloes of mass ≳1014 M⊙ today. These calculations are thousands of times more efficient than existing methods, are analytically controlled, and provide physical insights into the evolution of haloes with rapid early growth. Our constrained merger tree implementation is publicly available at https://github.com/galacticusorg/galacticus. [ABSTRACT FROM AUTHOR]