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Consider a robust retirement decision problem for a risk- and ambiguity-averse investor concerned about return ambiguity in risky asset prices. When the investor aims to maximize the worst-case scenario of his/her utility derived from consumption and bequest, we propose an optimal G-stopping approach to the robust optimization in a dual space with risk ambiguity. Under the G-expectation framework, we consider a reflected G-BSDE with an upper obstacle, which allows us to formulate a parabolic obstacle problem to the dual optimal stopping problem. From the dynamic result in the dual space, we establish the duality theorem to link between the primal problem with return ambiguity and the dual optimal stopping problem with risk ambiguity. We characterize the robust retirement time using the free boundary and derive the robust consumption and investment for a general class of utility functions. [ABSTRACT FROM AUTHOR]

This paper presents an inverse reinforcement learning (IRL) framework for Bayesian stopping time problems. By observing the actions of a Bayesian decision maker, we provide a necessary and sufficient condition to identify if these actions are consistent with optimizing a cost function. In a Bayesian (partially observed) setting, the inverse learner can at best identify optimality wrt the observed strategies. Our IRL algorithm identifies optimality and then constructs set-valued estimates of the cost function. To achieve this IRL objective, we use novel ideas from Bayesian revealed preferences stemming from microeconomics. We illustrate the proposed IRL scheme using two important examples of stopping time problems, namely, sequential hypothesis testing and Bayesian search. As a real-world example, we illustrate using a YouTube dataset comprising metadata from 190000 videos how the proposed IRL method predicts user engagement in online multimedia platforms with high accuracy. Finally, for finite datasets, we propose an IRL detection algorithm and give finite sample bounds on its error probabilities. [ABSTRACT FROM AUTHOR]

In this study, we consider an optimal control problem driven by a stochastic differential system with a stopping time terminal cost functional. To solve the optimal control problem under the stopping time terminal cost functional, we introduce a multi-time state optimal control systems, and prove that the multi-time state optimal control systems is a near-optimal control problem. We use the near-optimal control problem to take place the original optimal control problem under the cost functional with a stopping time terminal. Then, we establish the stochastic maximum principle for this kind of optimal control problem by introducing a discrete terminal system. Finally, we provide an example to describe the main results of this study. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimal stopping problems on semi-Markov processes (sMPs) with finite horizon and aim to establish the existence and algorithm of optimal stopping times. The key method is the equivalence between optimal stopping problems on sMPs and a special class of semi-Markov decision processes (sMDPs). We first introduce the optimality equation and show the existence of the optimal policies of finite-horizon sMDPs with additional terminal costs. Based on the optimal stopping problems on sMPs, we give an explicit construction of sMDPs such that the optimal stopping times of sMPs are equivalent to the optimal policies of the constructed sMDPs. Then, using the results of sMDPs developed here, we not only prove the existence of the optimal stopping times of sMPs, but also provide an algorithm for computing the optimal stopping times of sMPs. Moreover, we show that the optimal and ε -optimal stopping time can be characterized by the hitting time of some special sets. Finally, we give an example to illustrate the effectiveness of our conclusions. [ABSTRACT FROM AUTHOR]

This paper attempts to study the optimal stopping time for semi-Markov processes (SMPs) under the discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of the equivalent semi-Markov decision processes (SMDPs). The equivalence is embodied in the expected discounted cost functions of SMPs and SMDPs, that is, every stopping time of SMPs can induce a policy of SMDPs such that the value functions are equal, and vice versa. The existence of the optimal stopping time of SMPs is proved by this equivalence relation. Next, we give the optimality equation of the value function and develop an effective iterative algorithm for computing it. Moreover, we show that the optimal and ε-optimal stopping time can be characterized by the hitting time of the special sets. Finally, to illustrate the validity of our results, an example of a maintenance system is presented in the end. [ABSTRACT FROM AUTHOR]

In this paper, we consider a zero-sum differential game that can be stopped by any of the participants at one of time points known in advance. The cost functional may depend both on the time when the game ends and the position of the system at that time and on the player who initiates the game stopping. When optimizing the expectation of this functional, each player, based on the information the player has about the realized trajectory of the system, makes decisions both about his/her probability of stopping the game and about his/her own control of the conflict-controlled system; however, nondeterministic distribution rules are also allowed. The existence of the game value is shown under the assumption of a saddle point condition in the small game (the Isaacs condition). The construction of a stochastic guide whose model is a continuous-time Markov chain was used to construct approximately optimal strategies for the players. [ABSTRACT FROM AUTHOR]

In this paper we will give a simple stopping time proof in the Rd setting of the matrix weighted Triebel-Lizorkin bounds proved by F. Nazarov–S. Treil and A. Volberg, respectively. Furthermore, we provide explicit matrix Ap characteristic dependence and also discuss some interesting open questions. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying stopping time problem of interval-valued differential equation. Based on length constraint, we discuss the stopping time without Lipschitz condition, monotonicity and nonnegativity hypotheses. Then, stopping times with respects to upper and lower boundednesses are studied without monotonicity hypothesis, which is necessary in [27]. The results can be applied to discuss stopping time problem of more general interval-valued differential equations. We also provide some examples to verify our results. [ABSTRACT FROM AUTHOR]

We start proceeding with the stopping time theory in discrete time with the help of the Mizar system [1], [4]. We prove, that the expression for two stopping times k1 and k2 not always implies a stopping time (k1 + k2) (see Theorem 6 in this paper). If you want to get a stopping time, you have to cut the function e.g. (k1 + k2) ∪ T (see [2, p. 283 Remark 6.14]). Next we introduce the stopping time in continuous time. We are focused on the intervals [0, r] where r ∈ R. We prove, that for I = [0, r] or I = [0,+∞[ the set {A ⋂ I : A ∈ Borel-Sets} is a σ-algebra of I (see Definition 6 in this paper, and more general given in [3, p.12 1.8e]). The interval I can be considered as a timeline from now to some point in the future. This set is necessary to define our next lemma. We prove the existence of the σ-algebra of the τ -past, where τ is a stopping time (see Definition 11 in this paper and [6, p.187, Definition 9.19]). If τ1 and τ2 are stopping times with τ1 is smaller or equal than τ2 we can prove, that the σ-algebra of the τ1-past is a subset of the σ-algebra of the τ2-past (see Theorem 9 in this paper and [6, p.187 Lemma 9.21]). Suppose, that you want to use Lemma 9.21 with some events, that never occur, see as a comparison the paper [5] and the example for ST(1)={+∞} in the Summary. We don't have the element +1 in our above-mentioned time intervals [0, r[ and [0,+1[. This is only possible if we construct a new σ-algebra on R ∪ {−∞,+∞}. This construction is similar to the Borel-Sets and we call this σ-algebra extended Borel sets (see Definition 13 in this paper and [3, p. 21]). It can be proved, that {+∞} is an Element of extended Borel sets (see Theorem 21 in this paper). Now we use the interval [0,+∞] as a basis. We construct a σ-algebra on [0,+∞] similar to the book ([3, p. 12 18e]), see Definition 18 in this paper, and call it extended Borel subsets. We prove for stopping times with this given σ-algebra, that for τ1 and τ2 are stopping times with τ1 is smaller or equal than τ2 we have the σ-algebra of the τ1-past is a subset of the σ-algebra of the τ2-past, see Theorem 25 in this paper. It is obvious, that {+∞} 2 extended Borel subsets. In general, Lemma 9.21 is important for the proof of the Optional Sampling Theorem, see 10.11 Proof of (i) in [6, p. 203]. [ABSTRACT FROM AUTHOR]

. We start with the definition of stopping time according to [4], p.283. We prove, that different definitions for stopping time can coincide. We give examples of stopping time using constant-functions or functions defined with the operator max or min (defined in [6], pp.37-38). Finally we give an example with some given filtration. Stopping time is very important for stochastic finance. A stopping time is the moment, where a certain event occurs ([7], p.372) and can be used together with stochastic processes ([4], p.283). Look at the following example: we install a function ST: {1,2,3,4} → {0, 1, 2} ∪ {+∞}, we define:. a. ST(1)=1, ST(2)=1, ST(3)=2, ST(4)=2. b. The set {0,1,2} consists of time points: 0=now, 1=tomorrow, 2=the day after tomorrow. We can prove: c. {w, where w is Element of Ω: ST.w=0}=ø & {w, where w is Element of Ω: ST.w=1}={1,2} & {w, where w is Element of Ω: ST.w=2}={3,4} and ST is a stopping time. We use a function Filt as Filtration of {0,1,2}, Σ where Filt(0)=Ωnow, Filt(1)=Ωfut1 and Filt(2)=Ωfut2. From a.,b. and c. we know that: d. {w, where w is Element of Ω: ST.w=0} in Ωnow and {w, where w is Element of Ω: ST.w=1} in Ωfut1 and {w, where w is Element of Ω: ST.w=2} in Ωfut2. The sets in d. are events, which occur at the time points 0(=now), 1(=tomorrow) or 2(=the day after tomorrow), see also [7], p.371. Suppose we have ST(1)=+∞, then this means that for 1 the corresponding event never occurs. As an interpretation for our installed functions consider the given adapted stochastic process in the article [5]. ST(1)=1 means, that the given element 1 in {1,2,3,4} is stopped in 1 (=tomorrow). That tells us, that we have to look at the value f2(1) which is equal to 80. The same argumentation can be applied for the element 2 in {1,2,3,4}. ST(3)=2 means, that the given element 3 in {1,2,3,4} is stopped in 2 (=the day after tomorrow). That tells us, that we have to look at the value f3(3) which is equal to 100. ST(4)=2 means, that the given element 4 in {1,2,3,4} is stopped in 2 (=the day after tomorrow). That tells us, that we have to look at the value f3(4) which is equal to 120. In the real world, these functions can be used for questions like: when does the share price exceed a certain limit? (see [7], p.372). [ABSTRACT FROM AUTHOR]

Two optimal stopping problems for geometric random walks with the observer's power payoff function, on the finite and infinite horizons, are solved. For these problems, an explicit form of the cut value and also optimal stopping rules are established. It is proved that the optimal stopping rules are nonrandomized thresholds and describe the corresponding free boundary. An explicit form of the free boundary is presented. [ABSTRACT FROM AUTHOR]

This paper considers a multiple stopping time problem for a Markov chain observed in noise, where a decision maker chooses at most L stopping times to maximize a cumulative objective. We formulate the problem as a Partially Observed Markov Decision Process (POMDP) and derive structural results for the optimal multiple stopping policy. The main results are as follows: (i) The optimal multiple stopping policy is shown to be characterized by threshold curves Γ l , for l = 1 , … , L , in the unit simplex of Bayesian Posteriors. (ii) The stopping sets S l (defined by the threshold curves Γ l ) are shown to exhibit the following nested structure S l − 1 ⊂ S l . (iii) The optimal cumulative reward is shown to be monotone with respect to the copositive ordering of the transition matrix. (iv) A stochastic gradient algorithm is provided for estimating linear threshold policies by exploiting the structural results. These linear threshold policies approximate the threshold curves Γ l , and share the monotone structure of the optimal multiple stopping policy. (v) Application of the multiple stopping framework to interactively schedule advertisements in live online social media. It is shown that advertisement scheduling using multiple stopping performs significantly better than currently used methods. [ABSTRACT FROM AUTHOR]

Stopping-time Banach spaces is a collective term for the class of spaces of eventually null integrable processes that are defined in terms of the behaviour of the stopping times with respect to some fixed filtration. From the point of view of Banach space theory, these spaces in many regards resemble the classical spaces such as L 1 or C (Δ) , but unlike these, they do have unconditional bases. In the present paper, we study the canonical bases in the stopping-time spaces in relation to factorising the identity operator thereon. Since we work exclusively with the dyadic-tree filtration, this setup enables us to work with tree-indexed bases rather than directly with stochastic processes. En route to the factorisation results, we develop general criteria that allow one to deduce the uniqueness of the maximal ideal in the algebra of operators on a Banach space. These criteria are applicable to many classical Banach spaces such as (mixed-norm) L p -spaces, BMO, S L ∞ , and others. [ABSTRACT FROM AUTHOR]

In this work, we consider a stochastic differential equation that generalizes the well known Paris’ equation from fracture of materials. The model describes the propagation of cracks on solids, and it includes a deterministic summand and a stochastic component in terms of a Brownian motion. The use of Itô’s stochastic integral gives an equivalent stochastic integral equation that is further generalized here. We note that the probability distribution of the stopping time of the general model satisfies a deterministic diffusion–advection partial differential equation for which the solution is known only in a reduced number of particular cases. Motivated by these analytical results, we develop a fast finite-difference method to approximate the distribution of the stopping time. The method is an explicit exponential-like technique that preserves the main features of a probability distribution, namely, the non-negativity, the boundedness from above by 1 as well as the spatial monotonicity. Moreover, the method is a monotone technique that is also capable of preserving the temporal monotonicity of the approximations. These properties of the proposed methodology are thoroughly established in the present manuscript. A continuity condition of the numerical solutions in terms of the initial conditions and the temporal computational parameter is established also, together with a limiting property of the methodology when the free parameter tends to infinity. For comparison purposes, we are providing an implicit and stable discretization of the mathematical model which has a second order of convergence but for which conditions that guarantee the positivity, the boundedness and the monotonicity of approximations are not available. The numerical simulations obtained with implementations of our techniques show that the explicit method is an efficient scheme that preserves the characteristics of interest (non-negativity, boundedness from above by 1 and monotonicity), and that the numerical approximations are in good agreement with the known exact solutions. [ABSTRACT FROM AUTHOR]

The velocity distribution in the vicinity of the surface of an axisymmetric body rotating in a viscous medium at frequency ω directed along its axis is determined. The dissipative function has been calculated and used for deriving the equation of motion, from which an analytic expression for the stopping time of the body (until its complete stoppage) is obtained. The time of entrainment of an external stationary cylinder coaxial with the body is calculated by solving the time-dependent Navier-Stokes equation. [ABSTRACT FROM AUTHOR]

In this paper, we consider a size-dependent renewal risk model with stopping time claim-number process. In this model, we do not make any assumption on the dependence structure of claim sizes and inter-arrival times. We study large deviations of the aggregate amount of claims. For the subexponential heavy-tailed case, we obtain a precise large-deviation formula; our method substantially relies on a martingale for the structure of our models. [ABSTRACT FROM AUTHOR]

Departing from a general stochastic differential equation with Brownian diffusion, we establish that the distribution of probability of the stopping time is governed by a parabolic partial differential equation. A particular form of the problem under investigation may be associated to a stochastic generalization of the well-known Paris' law from structural mechanics, in which case, the solution of the boundary-value problem represents the probability distribution of the hitting time. An implicit, convergent and probability-based discretization to approximate the solution of the boundary-value problem is proposed in this work. Using a convenient vector representation of our scheme, we prove that the method preserves the most relevant properties of a probability distribution function, namely, the non-negativity, the boundedness from above by 1, and the monotonicity. In addition, we establish that our method is a convergent technique, and provide some illustrative comparisons against known exact solutions. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to present a novel method to estimate the optimal software testing time which minimizes the relevant expected software cost via a refined neural network approach with the grouped data, where the multi-stage look ahead prediction is carried out with a simple three-layer perceptron neural network with multiple outputs.Design/methodology/approach To analyze the software fault count data which follows a Poisson process with unknown mean value function, the authors transform the underlying Poisson count data to the Gaussian data by means of one of three data transformation methods, and predict the cost-optimal software testing time via a neural network.Findings In numerical examples with two actual software fault count data, the authors compare the neural network approach with the common non-homogeneous Poisson process-based software reliability growth models. It is shown that the proposed method could provide a more accurate and more flexible decision making than the common stochastic modeling approach.Originality/value It is shown that the neural network approach can be used to predict the optimal software testing time more accurately. [ABSTRACT FROM AUTHOR]

We consider the quickest change-point detection problem where the aim is to detect the onset of a prespecified drift in “live”-monitored standard Brownian motion; the change-point is assumed unknown (nonrandom). The object of interest is the distribution of the stopping time associated with the Generalized Shryaev–Roberts (GSR) detection procedure set up to “sense” the presence of the drift in the Brownian motion under surveillance. Specifically, we seek the GSR stopping time's survival function (the tail probability that no alarm is triggered by the GSR procedure prior to a given point in time), and distinguish two scenarios: (a) when the drift never sets in (prechange regime) and (b) when the drift is in effect ab initio (postchange regime). Under each scenario, we obtain a closed-form formula for the respective survival function, with the GSR statistic's (deterministic) nonnegative headstart assumed arbitrarily given. The two formulae are found analytically, through direct solution of the respective Kolmogorov forward equation via the Fourier spectral method to achieve separation of the spacial and temporal variables. We then exploit the obtained formulae numerically and characterize the pre- and postchange distributions of the GSR stopping time depending on three factors: (1) magnitude of the drift, (2) detection threshold, and (3) the GSR statistic's headstart. [ABSTRACT FROM PUBLISHER]

When to stop testing is an important aspect in software test management. This paper discusses a new approach to this problem. There are two major improvements in this approach in comparison to the earlier studies. It uses failure size proportional model to estimate the number of failures and the corresponding cost of repair. Instead of reliability it uses a new measure called attained failure size. Failure size is the probability of finding a failure causing input in the input domain. Attained failure size is the failure size at the termination of testing. The advantages of these improvements are also discussed. [ABSTRACT FROM AUTHOR]

In this paper we prove that Page's stopping time (CUSUM test) is optimal for detecting the changes in Markov processes that have invariant distribution. [ABSTRACT FROM AUTHOR]

A general scale-space algorithm is presented for denoising signals and images with spatially varying dominant scales. The process is formulated as a partial differential equation with spatially varying time. The proposed adaptivity is semilocal and is in conjunction with the classical gradient-based diffusion coefficient, designed to preserve edges. The new algorithm aims at maximizing a local SNR measure of the denoised image. It is based on a generalization of a global stopping time criterion presented recently by the author and his colleagues. Most notably, the method also works well for partially textured images and outperforms any selection of a global stopping time. Given an estimate of the noise variance, the procedure is automatic and can be applied well to most natural images. [ABSTRACT FROM AUTHOR]

One method successfully employed to denoise digital images is the diffusive iterative filtering. An important point of this technique is the estimation of the stopping time of the diffusion process. In this paper, we propose a stopping time criterion based on the evolution of the negentropy of the 'noise signal' with the diffusion parameter. The nonlinear diffusive filter implemented with this stopping criterion is evaluated by using several noisy test images with different statistics. Assuming that images are corrupted by additive Gaussian noise, a statistical measure of the Gaussianity can be used to estimate the amount of noise removed from noisy images. In particular, the differential entropy function or, equivalently, the negentropy are robust measures of the Gaussianity. Because of computational complexity of the negentropy function, it is estimated by using an approximation of the negentropy introduced by Hyvärinen in the context of independent component analysis. [ABSTRACT FROM AUTHOR]

We show that the optimal stopping time in the full-information optimal stopping problem of N independent identically distributed random variables has the asymptotic properties EτN ≈ N⁄3, DτN ≈ N²⁄18. [ABSTRACT FROM AUTHOR]

In this paper we deal with the optimal bankruptcy problem for agents who can optimally allocate their consumption rate, the amount of capital invested in the risky asset, as well as their leisure time. In our framework, the agents are endowed by an initial debt, and they are required to repay their debt continuously. Declaring bankruptcy, the debt repayment is exempted at the cost of a wealth shrinkage. We implement the duality method to solve the problem analytically and conduct a sensitivity analysis to the bankruptcy cost and benefit parameters. Introducing the flexible leisure/working rate, and therefore the labour income, into the bankruptcy model, we investigate its effect on the optimal strategies. [ABSTRACT FROM AUTHOR]

Background: The Elliot wave principle commonly characterizes the impulsive and corrective wave trends for both financial market trends and electrocardiograms. The impulsive wave trends of electrocardiograms can annotate several wave components of heart-beats including pathological heartbeat waveforms. The stopping time inquires which ordinal element satisfies the assumed mathematical condition within a numerical set. The proposed work constitutes several algorithmic states in reinforcement learning from the stopping time decision, which determines the impulsive wave trends. Each proposed algorithmic state is applicable to any relevant algorithmic state in reinforcement learning with fully numerical explanations. Because commercial electrocardiographs still misinterpret myocardial infarctions from extraordinary electrocardiograms, a novel algorithm needs to be developed to evaluate myocardial infarctions. Moreover, differential diagnosis for right ventricle infarction is required to contraindicate a medication such as nitroglycerin.Methods: The proposed work implements the stopping time theory to impulsive wave trend distribution. The searching process of the stopping time theory is equivalent to the actions toward algorithmic states in reinforcement learning. The state value from each algorithmic state represents the numerically deterministic annotated results from the impulsive wave trend distribution. The shape of the impulsive waveform is evaluated from the interoperable algorithmic states via least-first-power approximation and approximate entropy. The annotated electrocardiograms from the impulsive wave trend distribution utilize a structure of neural networks to approximate the isoelectric baseline amplitude value of the electrocardiograms, and detect the conditions of myocardial infarction. The annotated results from the impulsive wave trend distribution consist of another reinforcement learning environment for the evaluation of impulsive waveform direction.Results: The accuracy to discern myocardial infarction was found to be 99.2754% for the data from the comma-separated value format files, and 99.3579% for those containing representative beats. The clinical dataset included 276 electrocardiograms from the comma-separated value files and 623 representative beats.Conclusions: Our study aims to support clinical interpretation on 12-channel electrocardiograms. The proposed work is suitable for a differential diagnosis under infarction in the right ventricle to avoid contraindicated medication during emergency. An impulsive waveform that is affected by myocardial infarction or the electrical direction of electrocardiography is represented as an inverse waveform. [ABSTRACT FROM AUTHOR]

To extract full information from samples of DNA sequence data, it is necessary to use sophisticated model-based techniques such as importance sampling under the coalescent. However, these are limited in the size of datasets they can handle efficiently. Chen and Liu (2000) introduced the idea of stopping-time resampling and showed that it can dramatically improve the efficiency of importance sampling methods under a finite-alleles coalescent model. In this paper, a new framework is developed for designing stopping-time resampling schemes under more general models. It is implemented on data both from infinite sites and stepwise models of mutation, and extended to incorporate crossover recombination. A simulation study shows that this new framework offers a substantial improvement in the accuracy of likelihood estimation over a range of parameters, while a direct application of the scheme of Chen and Liu (2000) can actually diminish the estimate. The method imposes no additional computational burden and is robust to the choice of parameters. [ABSTRACT FROM AUTHOR]

Abstract: We consider the optimal double stopping time problem for each stopping time S. Following the optimal one stopping time problem, we study the existence of optimal stopping times and give a method to compute them. The key point is the construction of a new reward ϕ such that . [Copyright &y& Elsevier]

We develop a novel time-selection strategy for iterative image restoration techniques: the stopping time is chosen so that the correlation of signal and noise in the filtered image is minimized. The new method is applicable to any images where the noise to be removed is uncorrelated with the signal, under the assumptions that the filter used is suitable for the given type of data, and that neither the additive noise nor the filtering procedure alter the average gray value; no other knowledge (e.g. the noise variance, training data etc.) is needed. We analyse the theoretical properties of the method, then test the performance of our time estimation procedure experimentally, and demonstrate that it yields near-optimal results for a wide range of noise levels and for various filtering methods. [ABSTRACT FROM AUTHOR]

We formulate a robust optimal stopping-time problem for a state-space system and give the connection between various notions of lower value function for the associated games (and storage function for the associated dissipative system) with solutions of the appropriate variational inequality (VI) (the analogue of the Hamilton-Jacobi-Bellman-Isaacs equation for this setting). We show that the stopping-time rule can be obtained by solving the VI in the viscosity sense and a positive definite supersolution of the VI can be used for stability analysis. [ABSTRACT FROM AUTHOR]

Automated condition monitoring of active components of a system can improve the cost-efficiency of preventive and corrective maintenance and the availability of the production system. The validity, reliability and correct interpretation of the signals obtained from the condition monitoring instrumentation is important for the realisation of the potential benefits. The utilisation of experts in the interpretation of the condition monitoring signals is therefore crucial.In the paper, a stopping time model is formulated, where experts'' judgements on the remaining operating time of a component, given an indication of incipient failure, are utilised to arrive at optimal operational maintenance decisions. Optimality is defined in the sense of maximising expected utility. An expert model is also formulated, which utilises percentile information elicited from the experts. The modelling framework allows for the testing of different modelling assumptions which affect the decision outcomes. [ABSTRACT FROM AUTHOR]

Electronic markets are virtual frameworks where entities not known in advance have the opportunity to interact for the trading of products or services. Usually, a negotiation is necessary for the conclusion of the transaction. The conclusion is either positive (agreement) or negative (conflict). An efficient reasoning mechanism is necessary for players participating in negotiations. In this paper, we focus on the buyer side and propose two decision models based on the optimal stopping theory (OST). OST is proved to be very efficient in cases where an entity tries to find the time to stop a process with the aim of maximizing her utility. The outcome of the proposed decision method indicates whether the buyer stops a negotiation either by accepting the offer or continuing in the negotiation by rejecting it. In our models, we assume zero knowledge on the players' characteristics. Our proposed decision models do not require any complex modeling or any information provided by experts. Experimental results reveal the efficiency of each model and provide a comparison assessment with other research efforts. [ABSTRACT FROM AUTHOR]

We present a new model of stopping times and American options. In so doing, we solve a free-boundary problem. [ABSTRACT FROM AUTHOR]

We analyze the article by Han and Tsung (2009) 'The Optimal Stopping Time for Detecting Changes in Discrete Time Markov Processes,' and demonstrate that it is seriously flawed. [ABSTRACT FROM AUTHOR]

As an image-making tool for scientists studying the transient, instantaneous photography has long been seen as opening up a visual realm previously inaccessible to the inferior testimony of the human eye. But when photographic pioneer Henry Fox Talbot took the first photograph of a moving object by the light of an electric spark in 1851, he was guided by existing visual practices designed to create instantaneous vision in the eye itself. Exploring the background behind the peculiar subject of his experiment – a mechanically spinning disc – reveals a hidden prehistory of spark-illuminated photography: physicists’ pre-photographic techniques for stopping time. [Copyright &y& Elsevier]

Abstract: We prove the existence of a solution for the obstacle problem associated with the Kolmogorov operator corresponding to the stopping-time problem for stochastic Navier–Stokes equations in 2-D. [Copyright &y& Elsevier]

We consider denoising applications using nonlinear diffusion filters of BV type. Using the multiple timescales method, an equation is derived that approximates the time evolution of the image noise. Analysis of the corresponding variational inequality leads to an estimate of the timescale over which the noise decays to its local mean, given in terms of the filter parameters. We present a number of computed examples that demonstrate the validity of our stopping time estimate. [ABSTRACT FROM AUTHOR]

In this paper we consider two stochastic models of games which include martingales in the limit and games fairer with time. It turns out that there is a close relationship between them. This remark together with a stopping time technique allows us to obtain some limit theorems of Doob's type for these models. [ABSTRACT FROM AUTHOR]

This paper presents an approach to image filtering based on an optimal stopping time problem for the evolution equation describing the filtering kernel. This approach allows us to obtain easily an adaptivity of the filter with respect to the noise level. Well-posedness of the problem and convergence of fully discrete approximations are proved and numerical examples are presented and discussed. [ABSTRACT FROM AUTHOR]

A literary criticism of the poem "Iliad" by Homer is presented. It examines the immortality of the persona Achilles characterized by pain and mortality, and evaluates the factors influencing the travel made by the dramatist Priam towards the Lord of the Dead, Hades. It also mentions the prediction of the mother of Achilles in Book XVIII. An overview of the death of Achilles is also given.

In protoplanetary disks, zones of dense particle configuration promote planet formation. Solid particles in dense clouds alter their motion through collective effects and back reaction to the gas. The effect of particle-gas feedback with an ambient solid-to-gas ratios ϵ > 1 on the stopping time of particles is investigated. In experiments on board the International Space Station we studied the evolution of a dense granular gas while interacting with air. We observed diffusion of clusters released at the onset of an experiment but also the formation of new dynamical clusters. The solid-to-gas mass ratio outside the cluster varied in the range of about ϵ avg ~ 2.5–60. We find that the concept of gas drag in a viscous medium still holds, even if the medium is strongly dominated in mass by solids. However, a collective factor has to be used, depending on ϵ avg , i.e. the drag force is reduced by a factor 18 at the highest mass ratios. Therefore, flocks of grains in protoplanetary disks move faster and collide faster than their constituents might suggest. [ABSTRACT FROM AUTHOR]

Fixed-horizon planning considers a weighted graph and asks to construct a path that maximizes the sum of weights for a given time horizon T. However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution such that the expected stopping time is T. If the stopping-time distribution is not known, then to ensure robustness, the distribution is chosen by an adversary as the worst-case scenario. A stationary plan for every vertex always chooses the same outgoing edge. For fixed horizon or fixed stopping-time distribution, stationary plans are not sufficient for optimality. Quite surprisingly we show that when an adversary chooses the stopping-time distribution with expected stopping-time T , then stationary plans are sufficient. While computing optimal stationary plans for fixed horizon is NP-complete, we show that computing optimal stationary plans under adversarial stopping-time distribution can be achieved in polynomial time. [ABSTRACT FROM AUTHOR]

Summary The paper presents a method for computing the distribution of the stopping time for the Bayesian sequential one step look-ahead procedure with the proportion as parameter. [ABSTRACT FROM AUTHOR]

Let τ be the first exit time of a diffusion x(t) from a bounded domain Ω ⊂ IRn. This paper demonstrates that certain integral functionals ψ → E[∫τ0 ψ(t)dt | x(0) = x], ψ: [0, ∞) → IR, may be characterized as solutions to elliptic boundary value problems. The result is established using probabilistic arguments together with results from the theory of partial differential equations. One particular functional, a stochastic analogue of the Fourier transform, is analyzed carefully. Its basic computational properties, including an inversion formula, are developed. [ABSTRACT FROM AUTHOR]

We provide estimates on the rate of convergence for approximation schemes for Bellman equations associated with optimal stopping of controlled diffusion processes. These results extend (and slightly improve) the recent results by Barles & Jakobsen to the more difficult time-dependent case. The added difficulties are due to the presence of boundary conditions (initial conditions!) and the new structure of the equation which is now a parabolic variational inequality. The method presented is purely analytic and rather general and is based on earlier work by Krylov and Barles & Jakobsen. As applications we consider so-called control schemes based on the dynamic programming principle and finite difference methods (though not in the most general case). In the optimal stopping case these methods are similar to the Brennan & Schwartz scheme. A simple observation allows us to obtain the optimal rate 1/2 for the finite difference methods, and this is an improvement over previous results by Krylov and Barles & Jakobsen. Finally, we present an idea that allows us to improve all the above-mentioned results in the linear case. In particular, we are able to handle finite difference methods with variable diffusion coefficients without the reduction of order of convergence observed by Krylov in the nonlinear case. [ABSTRACT FROM AUTHOR]

Studies the tension between the claim that Article V of the U.S. Constitution articulates the exclusive procedure by which the Constitution may be amended and the historical commitment of the U.S. to the ideal that the people are sovereign. Background on Article V; Political positions on the resolution of Representative Thomas Corwin of Ohio to amend the U.S. Constitution; Efficacy of the Corwin amendment.

Forward genetic analyses in flies and mice have uncovered conserved transcriptional feedback loops at the heart of circadian pacemakers. Conserved mechanisms of posttranslational regulation, most notably phosphorylation, appear to be important for timing feedback. Transcript analyses have indicated that circadian clocks are not restricted to neurons but are found in several tissues. Comparisons between flies and mice highlight important differences in molecular circuitry and circadian organization. Future studies of pacemaker mechanisms and their control of physiology and behavior will likely continue to rely on forward genetics. [ABSTRACT FROM AUTHOR]

Data often come in the form of a longitudinal series, say N(⋅), whose observation has been "stopped" either by a terminal event U (e.g., death) or censoring event C (e.g., lost to follow-up). When N(⋅) is not deterministic, it is generally not possible to use standard survival analysis tools (e.g., the Kaplan-Meier estimator) to consistently estimate functionals of the distribution of N(U) because of "induced" informative censoring. Various seemingly unrelated estimators recently have been proposed to handle this difficulty within the context of specific problems, ranging from the analysis of quality-adjusted survival data to recurrent event data to lifetime medical cost data. In this article I consider a general framework containing each of these specific examples as a special case, propose a class of estimators for the mean of the stopped longitudinal process, and establish the asymptotic properties of this class of estimators. Connections between the aforementioned estimators are established, and questions related to asymptotic relative efficiency of the various estimators are addressed. Based on these results, I propose some new estimators with finite-sample optimality properties. Finally, I investigate the utility of the proposed estimators in two simulated examples, and discuss potential extensions of this work. [ABSTRACT FROM AUTHOR]