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Equity crowdfunding campaign overfunding occurs when a campaign generates funds in excess of the funding goal and has hence been touted as the mark of an extraordinarily successful campaign. However, a novel theoretical lens is needed to comprehend funders' enthusiasm in their support of such campaigns. Building on the extant literature on contagion effect, we constructed a research model that posits confidence contagion invoked by confidence cues embedded in campaign materials as a key driver of overfunding. Our hypotheses were validated in two complementary empirical studies. In Study 1, we manipulated confidence cues in a controlled experiment to verify the activation of confidence contagion at the individual level. Analytical results indicate that individual funders detect self-confidence traits from confidence cues embedded in campaign materials and assimilate the fundraiser's confidence via a spontaneous social appraisal mechanism. In turn, confidence contagion drives funders to congregate and invest in campaigns. In Study 2, we analyzed a secondary dataset collected from a leading equity crowdfunding platform to discern how confidence contagion drives overfunding at the collective level. By modeling funding activities as a Hawkes process, we derived three key metrics that govern the emergence and magnitude of funding surges. We demonstrated that these metrics of funding surges mediate the impact of confidence cues on the level of overfunding for equity crowdfunding campaigns. The findings from this study could inform future research seeking to untangle the interdependencies between individual and collective mechanisms underlying crowd phenomena, provide strategic guidance to fundraisers interested in promoting the overfunding of their campaigns, and help crowdfunding platforms predict the potential extent of overfunding and advise fundraisers accordingly. [ABSTRACT FROM AUTHOR]

AbstractFueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the network estimates is critical in scientific applications, existing methodological and theoretical work has primarily addressed estimation. To bridge this gap, we develop a new statistical inference procedure for high-dimensional Hawkes processes. The key ingredient for the inference procedure is a new concentration inequality on the first- and second-order statistics for integrated stochastic processes, which summarize the entire history of the process. Combining recent martingale central limit theorem with the new concentration inequality, we then characterize the convergence rate of the test statistics in a continuous time domain. Finally, to account for potential non-stationarity of the process in practice, we extend our statistical inference procedure to a flexible class of Hawkes processes with time-varying background intensities and unknown transition functions. The finite sample validity of the inferential tools is illustrated via extensive simulations and further applied to a neuron spike train data set. [ABSTRACT FROM AUTHOR]

AbstractThis article studies the properties of Hawkes process with a gamma memory kernel and a shape parameter α∈(0,1]. This process, called rough Hawkes process, is nearly unstable since its intensity diverges to +∞ for a very brief duration when a jump occurs. First, we find conditions that ensure the stability of the process and provide a closed form expression of the expected intensity. Second, we next reformulate the intensity as an infinite dimensional Markov process. Approximating these processes by discretization and then considering the limit leads to the Laplace transform of the point process. This transform depends on the solution of an elegant fractional integro-differential equation. The fractional operator is defined by the gamma kernel and is similar to the left-fractional Riemann-Liouville integral. We provide a simple method for computing the Laplace transform. This is easily invertible by discrete Fourier transform so that the probability density of the process can be recovered. We also propose two methods of simulation. We conclude the article by presenting the log-likelihood of the rough Hawkes process and use it to fit hourly Bitcoin log-returns from 9/2/18 to 9/2/23. [ABSTRACT FROM AUTHOR]

Spatiotemporal events occur in many disciplines, including economics, sociology, criminology, and seismology, with different patterns in space and time related to environmental characteristics, policing, and human behavior. In this paper, we propose a class of multivariate Hawkes processes with spatial covariates to consider the influence structure of spatial features in spatiotemporal events and the spatiotemporal patterns such as clustering. Baseline intensities are assumed to be a spatial Poisson regression model to explain spatial feature influence. The transfer functions are considered unknown but smooth and decreasing to explain the clustering phenomena. A semiparametric estimation method based on time discretization and local constant approximation is introduced. Transfer function estimators are shown to be consistent, and baseline intensity estimators are consistent and asymptotically normal. We examine the numerical performance of the proposed estimators with extensive simulation and illustrate the application of the proposed model to crime data obtained from Pittsburgh, Pennsylvania. [ABSTRACT FROM AUTHOR]

Copyright of Telecommunications Science is the property of Beijing Xintong Media Co., Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The event sequences with spatiotemporal characteristics have been rapidly produced in various domains, such as earthquakes in seismology, electronic medical records in healthcare, and transactions in the financial market. These data often continue for weeks, months, or years, and the past events may trigger subsequent events. In this context, modeling the spatiotemporal event sequences and forecasting the next event has become a hot topic. However, existing models either failed to capture the long-term temporal dependencies or ignored the essential spatial information between sequences. In this paper, we proposed a novel graph transformer Hawkes process (GTHP) model to capture the long-term temporal dependencies and spatial information from historical events. The core concept of GTHP is to learn the spatial information by graph convolutional neural networks and capture long-term temporal dependencies from events embedding by self-attention mechanism. Moreover, we integrated the learned spatial information into the event embedding as auxiliary information. Numerous experiments on synthetic and real-world datasets proved the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Marked temporal point process models (MTPPs) aim to model event sequences and event markers (associated features) in continuous time. These models have been applied to various application domains where capturing event dynamics in continuous time is beneficial, such as education systems, social networks, and recommender systems. However, current MTPPs suffer from two major limitations, i.e., inefficient representation of event dynamic's influence on marker distribution and losing fine-grained representation of historical marker distributions in the modeling. Motivated by these limitations, we propose a novel model called Marked Point Processes with Memory-Enhanced Neural Networks (MoMENt) that can capture the bidirectional interrelations between markers and event dynamics while providing fine-grained marker representations. Specifically, MoMENt is constructed of two concurrent networks: Recurrent Activity Updater (RAU) to capture model event dynamics and Memory-Enhanced Marker Updater (MEMU) to represent markers. Both RAU and MEMU components are designed to update each other at every step to model the bidirectional influence of markers and event dynamics. To obtain a fine-grained representation of maker distributions, MEMU is devised with external memories that model detailed marker-level features with latent component vectors. Our extensive experiments on six real-world user interaction datasets demonstrate that MoMENt can accurately represent users' activity dynamics, boosting time, type, and marker predictions, as well as recommendation performance up to 76.5%, 65.6%, 77.2%, and 57.7%, respectively, compared to baseline approaches. Furthermore, our case studies show the effectiveness of MoMENt in providing meaningful and fine-grained interpretations of user-system relations over time, e.g., how user choices influence their future preferences in the recommendation domain. [ABSTRACT FROM AUTHOR]

Two key features of airline departure delays are that they cascade and that there can be exceptional peaks. We model these features using an intensity‐based Hawkes process. Our application to all KLM departure delays at Amsterdam Schiphol airport in January 2015 shows that volatility in departure delays is endogenous. We correlate the key parameters of the estimated Hawkes process with daily weather conditions and find that these conditions amplify the self‐exciting feature of departure delays. [ABSTRACT FROM AUTHOR]

The military medical evacuation (MEDEVAC) system is the primary method to evacuate time-sensitive combat casualties from the battlefield to appropriately staffed and equipped medical treatment facilities (MTFs). The intent of this paper is to analyze how MTF capability and capacity impact MEDEVAC system performance. We develop a self-exciting spatio-temporal Hawkes process model as well as a notional, synthetically generated MEDEVAC scenario of the post-Bosnian War to evaluate and compare eight distinct MEDEVAC dispatching and delivery policies within a high-intensity combat environment. The results garnered from this paper highlight the substantial impact MTFs have on MEDEVAC systems and should be considered in future research. [ABSTRACT FROM AUTHOR]

The rapid growth of earthquake catalogs, driven by machine learning-based phase picking and denser seismic networks, calls for the application of a broader range of models to determine whether the new data enhances earthquake forecasting capabilities. Additionally, this growth demands that existing forecasting models efficiently scale to handle the increased data volume. Approximate inference methods such as inlabru, which is based on the Integrated nested Laplace approximation, offer improved computational efficiencies and the ability to perform inference on more complex point-process models compared to traditional MCMC approaches. We present SB-ETAS: a simulation based inference procedure for the epidemic-type aftershock sequence (ETAS) model. This approximate Bayesian method uses sequential neural posterior estimation (SNPE) to learn posterior distributions from simulations, rather than typical MCMC sampling using the likelihood. On synthetic earthquake catalogs, SB-ETAS provides better coverage of ETAS posterior distributions compared with inlabru. Furthermore, we demonstrate that using a simulation based procedure for inference improves the scalability from O (n 2) to O (n log n) . This makes it feasible to fit to very large earthquake catalogs, such as one for Southern California dating back to 1981. SB-ETAS can find Bayesian estimates of ETAS parameters for this catalog in less than 10 h on a standard laptop, a task that would have taken over 2 weeks using MCMC. Beyond the standard ETAS model, this simulation based framework allows earthquake modellers to define and infer parameters for much more complex models by removing the need to define a likelihood function. [ABSTRACT FROM AUTHOR]

Consider a risk model in which the claims follow a non stationary arrival process that satisfies a large deviation principle. Supposing that the claim sizes form a sequence of i.i.d. random variables with subexponential tail, precise large deviations for the aggregate claims are obtained, by allowing the claim-sizes and claim inter-arrival (waiting) times to be arbitrarily dependent. [ABSTRACT FROM AUTHOR]

We use the Hawkes process to model the high-frequency price process of 108 stocks in the Chinese stock market, in order to understand the endogeneity of price changes and the mechanism of information processing. Using a piece-wise constant exogenous intensity, we employ non-parametric estimation, residual analysis, and Bayesian Information Criterion (BIC) to determine that a power-law kernel is the most appropriate for our data. We propose the internal branching ratio to represent endogeneity within a finite interval. The branching ratio tends to be higher after the market opens and before the market closes, with a mean value of around 0.81, suggesting significant endogeneity in price changes. In addition, we explore the relationship between branching ratios and stock characteristics using panel regression. Higher branching ratios are associated with lower levels of price efficiency at high, but not low, frequencies. Finally, the branching ratio increases over time without significant impact from COVID-19. [ABSTRACT FROM AUTHOR]

Amidst rising trading volumes, there's evident demand for volatility trading. This study assists Chinese stakeholders in understanding the iVIX's functionality, offering insights for investments and policy-making. Building on the VIX option pricing model, the research introduces a novel approach: the mean-reverting logarithmic stochastic volatility Hawkes jump model (MLSVHJ). Using VIX call option data from March 9, 2020, to March 18, 2021, the MLSVHJ model outperformed four others during 2020's three US market crashes. Additionally, this model's parameters aligned well with theoretical expectations. However, the positive correlation observed between the iVIX and the Shanghai Composite Index prompts a reevaluation of applying global VIX standards directly to China. [ABSTRACT FROM AUTHOR]

Connected and autonomous vehicles (CAVs) are advancing at a fast speed with the improvement of the automotive industry, which opens up new possibilities for different attacks. A Distributed Denial-of-Service (DDoS) attacker floods the in-vehicle network with fake messages, resulting in the failure of driving assistance systems and impairment of vehicle control functionalities, seriously disrupting the normal operation of the vehicle. In this paper, we propose a novel DDoS attack detection method for in-vehicle Ethernet Scalable service-Oriented Middleware over IP (SOME/IP), which integrates the Hawkes process with Long Short-Term Memory networks (LSTMs) to capture the dynamic behavioral features of the attacker. Specifically, we employ the Hawkes process to capture features of the DDoS attack, with its parameters reflecting the dynamism and self-exciting properties of the attack events. Subsequently, we propose a novel deep learning network structure, an HP-LSTM block, inspired by the Hawkes process, while employing a residual attention block to enhance the model's detection efficiency and accuracy. Additionally, due to the scarcity of publicly available datasets for SOME/IP, we employed a mature SOME/IP generator to create a dataset for evaluating the validity of the proposed detection model. Finally, extensive experiments were conducted to demonstrate the effectiveness of the proposed DDoS attack detection method. [ABSTRACT FROM AUTHOR]

We consider parallel single-server queues in heavy traffic with randomly split Hawkes arrival processes. The service times are assumed to be independent and identically distributed (i.i.d.) in each queue and are independent in different queues. In the critically loaded regime at each queue, it is shown that the diffusion-scaled queueing and workload processes converge to a multidimensional reflected Brownian motion in the non-negative orthant with orthonormal reflections. For the model with abandonment, we also show that the corresponding limit is a multidimensional reflected Ornstein–Uhlenbeck diffusion in the non-negative orthant. [ABSTRACT FROM AUTHOR]

In this paper, we consider a risk model with heavy-tailed claims and Brownian perturbation. Assuming that the distribution function of claim-size is subexponential, and the arrival process of claims is a non stationary process satisfying the principle of large deviation, the asymptotic formula for the ruin probability of this risk model at random time is obtained. [ABSTRACT FROM AUTHOR]

AbstractThe Hawkes process models have been recently become a popular tool for modeling and analysis of neural spike train data. Despite this popularity, existing methodological and theoretical work has mainly focused on models without assumption of time-varying covariates, such as stimulus drive. In this article, motivated by neuronal spike trains study in the presence of stimuli, we propose a new Hawkes process model, where covariates are included in the intensity function. We consider the problem of simultaneous variable selection and estimation for the Hawkes process in the high-dimensional regime. Estimation of the intensity function of the high-dimensional point process is considered within a nonparametric framework, applying B-splines and the SCAD penalty for matters of sparsity. We apply the Doob-Kolmogorov inequality to establish the consistency of the resulting estimators. Finally, we illustrate the performance of our proposal through simulation and demonstrate its utility by applying it to the neuron spike train data set. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The Hawkes process models have been recently become a popular tool for modeling and analysis of neural spike trains. In this article, motivated by neuronal spike trains study, we propose a novel multivariate generalized linear Hawkes process model, where covariates are included in the intensity function. We consider the problem of simultaneous variable selection and estimation for the multivariate generalized linear Hawkes process in the high-dimensional regime. Estimation of the intensity function of the high-dimensional point process is considered within a nonparametric framework, applying B-splines and the SCAD penalty for matters of sparsity. We apply the Doob-Kolmogorov inequality and the martingale central limit theory to establish the consistency and asymptotic normality of the resulting estimators. Finally, we illustrate the performance of our proposal through simulation and demonstrate its utility by applying it to the neuron spike train data set. [ABSTRACT FROM AUTHOR]

Classic diffusion processes fail to explain asset return volatility. Many empirical findings on asset return time series, such as heavy tails, skewness and volatility clustering, suggest decomposing the volatility of an asset's return into two components, one caused by a Brownian motion and another by a jump process. We analyze the sensitivity of European call options to memory and self-excitation parameters, underlying price, volatility and jump risks. We expand Heston's stochastic volatility model by adding to the instantaneous asset prices, a jump component driven by a Hawkes process with a kernel function or memory kernel that is a Fourier transform of a probability measure. This kernel function defines the memory of the asset price process. For instance, if it is fast decreasing, the contagion effect between asset price jumps is limited in time. Otherwise, the processes remember the history of asset price jumps for a long period. To investigate the impact of different rates of decay or types of memory, we consider four probability measures: Laplace, Gaussian, Logistic and Cauchy. Unlike Hawkes processes with exponential kernels, the Markov property is lost but stationarity is preserved; this ensures that the unconditional expected arrival rate of the jump does not explode. In the absence of the Markov property, we use the Fourier transform representation to derive a closed form expression of a European call option price based on characteristic functions. A numerical illustration shows that our extension of the Heston model achieves a better fit of the Euro Stoxx 50 option data than the standard version. [ABSTRACT FROM AUTHOR]

Modelling spatial and temporal patterns in ecology is imperative to understand the complex processes inherent in ecological phenomena. Log‐Gaussian Cox processes are a popular choice among ecologists to describe the spatiotemporal distribution of point‐referenced data. In addition, point pattern models where events instigate others nearby (i.e., self‐exciting behaviour) are becoming increasingly popular to infer the contagious nature of events (e.g., animal sightings). While there are existing R packages that facilitate fitting spatiotemporal point processes and, separately, self‐exciting models, none incorporate both. We present an R package, stelfi, that fits spatiotemporal self‐exciting and log‐Gaussian Cox process models using Template Model Builder through a range of custom‐written C++ templates. We illustrate the use of stelfi's functions fitting models to Sasquatch (bigfoot) sightings data within the USA. The structure of these data is typical of many seen in ecology studies. We show, from a temporal Hawkes process to a spatiotemporal self‐exciting model, how the models offered by the package enable additional insights into the temporal and spatial progression of point pattern data. We present extensions to these well‐known models that include spatiotemporal self‐excitation and joint likelihood models, which are better suited to capture the complex mechanisms inherent in many ecological data. The package stelfi offers user‐friendly functionality, is open source, and is available from CRAN. It offers the implementation of complex spatiotemporal point process models in R for applications even beyond the field of ecology. [ABSTRACT FROM AUTHOR]

Event sequences with spatiotemporal characteristics have been rapidly produced in various domains, such as earthquakes in seismology, electronic medical records in health care, and transactions in the financial market. These data are discrete events that are continuous and often continue for weeks, months, or years, and past events may trigger subsequent events. In this context, modeling spatiotemporal event sequences and forecasting the occurrence time and marker of the next event has become a hot topic. However, existing models either fail to capture the long-term temporal dependencies or ignore the essential spatial information between sequences. Moreover, existing models learn the influence of past events and predicted future events in Euclidean space, which has been shown to cause a significant distortion in hierarchical structure data. To correctly predict future events from historical events and design interventions and controls to guide the event dynamics to the desired results and inspired by the high capacity of modeling data in hyperbolic space, we proposed a novel hyperbolic graph transformer Hawkes process (HGTHP) model to capture the long-term temporal dependencies and spatial information from historical events with a hierarchical structure. The core concept of the HGTHP is to integrate the learned spatial information into the event embedding as auxiliary information and capture long-short term temporal dependencies from event sequences in non-Euclidean space by a hyperbolic self-attention mechanism. Numerous experiments on synthetic and real-world datasets proved that the proposed model obtains spatiotemporal information from hyperbolic space, and its predictions outperform those of state-of-the-art baselines in both time and marker, proving the proposed model's effectiveness. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of learning temporal graph representations, which capture the changing nature of complex evolving networks. Existing approaches mainly focus on adding new nodes and edges to capture dynamic graph structures. However, to achieve more accurate representation of graph evolution, we consider both the addition and deletion of nodes and edges as events. These events occur at irregular time scales and are modeled using temporal point processes. Our goal is to learn the conditional intensity function of the temporal point process to investigate the influence of deletion events on node representation learning for link-level prediction. We incorporate network entropy, a measure of node and edge significance, to capture the effect of node deletion and edge removal in our framework. Additionally, we leveraged the characteristics of a generalized temporal Hawkes process, which considers the inhibitory effects of events where past occurrences can reduce future intensity. This framework enables dynamic representation learning by effectively modeling both addition and deletion events in the temporal graph. To evaluate our approach, we utilize autonomous system graphs, a family of inhomogeneous sparse graphs with instances of node and edge additions and deletions, in a link prediction task. By integrating these enhancements into our framework, we improve the accuracy of dynamic link prediction and enable better understanding of the dynamic evolution of complex networks.

A novel estimator for the parameters governing spatial–temporal point processes is proposed. Unlike the maximum likelihood estimator, the proposed estimator is fast and easy to compute, and does not require the computation or approximation of a computationally expensive integral. This parametric estimator is based on the Stoyan–Grabarnik (sum of inverse intensity) statistic and is shown to be consistent, under quite general conditions. Simulations are presented demonstrating the performance of the estimator. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of learning temporal graph representations, which capture the changing nature of complex evolving networks. Existing approaches mainly focus on adding new nodes and edges to capture dynamic graph structures. However, to achieve more accurate representation of graph evolution, we consider both the addition and deletion of nodes and edges as events. These events occur at irregular time scales and are modeled using temporal point processes. Our goal is to learn the conditional intensity function of the temporal point process to investigate the influence of deletion events on node representation learning for link-level prediction. We incorporate network entropy, a measure of node and edge significance, to capture the effect of node deletion and edge removal in our framework. Additionally, we leveraged the characteristics of a generalized temporal Hawkes process, which considers the inhibitory effects of events where past occurrences can reduce future intensity. This framework enables dynamic representation learning by effectively modeling both addition and deletion events in the temporal graph. To evaluate our approach, we utilize autonomous system graphs, a family of inhomogeneous sparse graphs with instances of node and edge additions and deletions, in a link prediction task. By integrating these enhancements into our framework, we improve the accuracy of dynamic link prediction and enable better understanding of the dynamic evolution of complex networks. [ABSTRACT FROM AUTHOR]

We propose a new Kalikow decomposition for continuous-time multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation algorithms that hold either for stationary processes with potentially infinite network but bounded intensities, or for processes with unbounded intensities in a finite network and with empty past before zero. The Kalikow decomposition is not unique, and we discuss the choice of the decomposition in terms of algorithmic efficiency in certain cases. We apply these methods to several examples: the linear Hawkes process, the age-dependent Hawkes process, the exponential Hawkes process, and the Galves–Löcherbach process. [ABSTRACT FROM AUTHOR]

This article reviews some of the statistical issues involved with modeling SARS-CoV02 (Covid-19) in Los Angeles County, California, using Hawkes point process models and SEIR models. The two types of models are compared, and their pros and cons are discussed. We also discuss particular statistical decisions, such as where to place the upper limits on y-axes, and whether to use a Bayesian or frequentist version of the model, how to estimate seroprevalence, and fitting the density of transmission times in the Hawkes model. [ABSTRACT FROM AUTHOR]

This study proposes a versatile model for the dynamics of the best bid and ask prices using an extended Hawkes process. The model incorporates the zero intensities of the spread-narrowing processes at the minimum bid–ask spread, spread-dependent intensities, possible negative excitement, and nonnegative intensities. We apply the model to high-frequency best bid and ask price data from U.S. stock markets. The empirical findings demonstrate a spread-narrowing tendency, excitations of the intensities caused by previous events, the impact of flash crashes, characteristic trends in fast trading over time, and the different features of market participants in the various exchanges. [ABSTRACT FROM AUTHOR]

Abstract Modelling spatial and temporal patterns in ecology is imperative to understand the complex processes inherent in ecological phenomena. Log‐Gaussian Cox processes are a popular choice among ecologists to describe the spatiotemporal distribution of point‐referenced data. In addition, point pattern models where events instigate others nearby (i.e., self‐exciting behaviour) are becoming increasingly popular to infer the contagious nature of events (e.g., animal sightings). While there are existing R packages that facilitate fitting spatiotemporal point processes and, separately, self‐exciting models, none incorporate both. We present an R package, stelfi, that fits spatiotemporal self‐exciting and log‐Gaussian Cox process models using Template Model Builder through a range of custom‐written C++ templates. We illustrate the use of stelfi's functions fitting models to Sasquatch (bigfoot) sightings data within the USA. The structure of these data is typical of many seen in ecology studies. We show, from a temporal Hawkes process to a spatiotemporal self‐exciting model, how the models offered by the package enable additional insights into the temporal and spatial progression of point pattern data. We present extensions to these well‐known models that include spatiotemporal self‐excitation and joint likelihood models, which are better suited to capture the complex mechanisms inherent in many ecological data. The package stelfi offers user‐friendly functionality, is open source, and is available from CRAN. It offers the implementation of complex spatiotemporal point process models in R for applications even beyond the field of ecology.

In the era of big data, mathematical and scientific methods significantly contribute to educational reform, continuously revitalizing precision teaching. In this paper, we use the new Hawkes process to collect and vectorize data on how students learn. Then, we use the unique thermal coding method to combine the behavioral feature vector with the teaching feature vector. Finally, we classify the data and use the softmax function to predict the learning effect. Based on the prediction results, a mathematical model for precise teaching optimization of vocational education English has been established, and the decision function is used to solve the problem and optimize teaching methods. It was found that all the indicators of learning behavior characteristics of students in the experimental class applying the teaching method optimization model were significantly improved, and there was a significant difference at the level of 0.05 (P = 0.000

Exploring the digital development of art education can effectively enhance students’ creativity in art design. This paper constructs a digital teaching platform for art education based on big data technology and analyzes student learning behavior data in the teaching platform. For student learning behavior with a new Hawkes process for data extraction, the decomposition of the student learning effect is realized by data encoder, event-level decoder and course-level decoder. Performance tests and art teaching effect analysis were conducted for the platform built in this paper. From the performance test, the throughput of the test interface is 580 when the server CPU is maintained at about 26%, memory is maintained at about 48.62%, and load is maintained at about 4.7. From the teaching effect, the four dimensions of students’ creativity changes had significant differences; namely, the p-values of adventurousness, curiosity, imagination, and challenge were 0.189, 0.247, 0.076, and 0.425, respectively. This indicates that the digital teaching platform for art education built by using big data technology can effectively enhance students’ creativity and also provide a new direction for the digital development of art education.

Connected and autonomous vehicles (CAVs) are advancing at a fast speed with the improvement of the automotive industry, which opens up new possibilities for different attacks. A Distributed Denial-of-Service (DDoS) attacker floods the in-vehicle network with fake messages, resulting in the failure of driving assistance systems and impairment of vehicle control functionalities, seriously disrupting the normal operation of the vehicle. In this paper, we propose a novel DDoS attack detection method for in-vehicle Ethernet Scalable service-Oriented Middleware over IP (SOME/IP), which integrates the Hawkes process with Long Short-Term Memory networks (LSTMs) to capture the dynamic behavioral features of the attacker. Specifically, we employ the Hawkes process to capture features of the DDoS attack, with its parameters reflecting the dynamism and self-exciting properties of the attack events. Subsequently, we propose a novel deep learning network structure, an HP-LSTM block, inspired by the Hawkes process, while employing a residual attention block to enhance the model’s detection efficiency and accuracy. Additionally, due to the scarcity of publicly available datasets for SOME/IP, we employed a mature SOME/IP generator to create a dataset for evaluating the validity of the proposed detection model. Finally, extensive experiments were conducted to demonstrate the effectiveness of the proposed DDoS attack detection method.

Abstract Hawkes process is a class of self-exciting point processes with clustering effect whose jump rate relies on their entire past history. This process is usually defined as a continuous-time setting and has been widely applied in several fields, including insurance, finance, queueing theory, and statistics. The Hawkes model is generally non-Markovian because the future development of a self-exciting point process is determined by the timing of past events. However, it can be Markovian in special cases such as when the exciting function is an exponential function or a sum of exponential functions. Difficulty arises when the exciting function is not an exponential function or a sum of exponentials, in which case the process can be non-Markovian. The inverse Markovian case for Hawkes processes was introduced by Seol (Stat. Probab. Lett. 155:108580, 2019) who studied some asymptotic behaviors. An extended version of the inverse Markovian Hawkes process was also studied by Seol (J. Korean Math. Soc. 58(4):819–833, 2021). In the current work, we propose a class of Markovian self-exciting processes that interpolates between the Hawkes process and the inverse Hawkes process. We derived limit theorems for the newly considered class of Markovian self-exciting processes. In particular, we established both the law of large numbers (LLN) and central limit theorems (CLT) with some key results.

Hawkes process are very popular mathematical tools for modeling phenomena exhibiting a self‐exciting or self‐correcting behavior. Typical examples are earthquakes occurrence, wild‐fires, drought, capture‐recapture, crime violence, trade exchange, and social network activity. The widespread use of Hawkes process in different fields calls for fast, reproducible, reliable, easy‐to‐code techniques to implement such models. We offer a technique to perform approximate Bayesian inference of Hawkes process parameters based on the use of the R‐package inlabru. The inlabru R‐package, in turn, relies on the INLA methodology to approximate the posterior of the parameters. Our Hawkes process approximation is based on a decomposition of the log‐likelihood in three parts, which are linearly approximated separately. The linear approximation is performed with respect to the mode of the parameters' posterior distribution, which is determined with an iterative gradient‐based method. The approximation of the posterior parameters is therefore deterministic, ensuring full reproducibility of the results. The proposed technique only requires the user to provide the functions to calculate the different parts of the decomposed likelihood, which are internally linearly approximated by the R‐package inlabru. We provide a comparison with the bayesianETAS R‐package which is based on an MCMC method. The two techniques provide similar results but our approach requires two to ten times less computational time to converge, depending on the amount of data. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the pricing of basket-spread options with default risk under Hawkes jump-diffusion processes. A self-exciting Hawkes process is employed to describe jump clustering, and jump amplitudes of different assets in baskets are all correlated. In addition, the diffusive components of assets are also assumed to be correlated with each other. We obtain option prices by approximating the arithmetic average of the underlying assets in the basket with their second moment-matched geometric average values, and numerical experiments show that our approximated prices are quite accurate, spanning different underlying asset numbers and alternative strike prices. Finally, we illustrate the effects of default risk and clustered jump risk on the prices of basket-spread options. [ABSTRACT FROM AUTHOR]

Rampant terrorism poses a serious threat to the national security of many countries worldwide, particularly due to separatism and extreme nationalism. This paper focuses on the development and application of a temporal self-exciting point process model to the terror data of three countries: the US, Turkey, and the Philippines. To account for occurrences with the same time-stamp, this paper introduces the order mark and reward term in parameter selection. The reward term considers the triggering effect between events in the same time-stamp but different order. Additionally, this paper provides comparisons between the self-exciting models generated by day-based and month-based arrival times. Another highlight of this paper is the development of a model to predict the number of terror events using a combination of simulation and machine learning, specifically the random forest method, to achieve better predictions. This research offers an insightful approach to discover terror event patterns and forecast future occurrences of terror events, which may have practical application towards national security strategies. [ABSTRACT FROM AUTHOR]

Modeling Hawkes process using deep learning is superior to traditional statistical methods in the goodness of fit. However, methods based on RNN or self-attention are deficient in long-time dependence and recursive induction, respectively. Universal Transformer (UT) is an advanced framework to integrate these two requirements simultaneously due to its continuous transformation of self-attention in the depth of the position. In addition, migration of the UT framework involves the problem of effectively matching Hawkes process modeling. Thus, in this paper, an iterative convolutional enhancing self-attention Hawkes process with time relative position encoding (ICAHP-TR) is proposed, which is based on improved UT. First, the embedding maps from dense layers are carried out on sequences of arrival time points and markers to enrich event representation. Second, the deep network composed of UT extracts hidden historical information from event expression with the characteristics of recursion and the global receptive field. Third, two designed mechanics, including the relative positional encoding on the time step and the convolution enhancing perceptual attention are adopted to avoid losing dependencies between relative and adjacent positions in the Hawkes process. Finally, the hidden historical information is mapped by Dense layers as parameters in Hawkes process intensity function, thereby obtaining the likelihood function as the network loss. The experimental results show that the proposed methods demonstrate the effectiveness of synthetic datasets and real-world datasets from the perspective of both the goodness of fit and predictive ability compared with other baseline methods. [ABSTRACT FROM AUTHOR]

The assessment of the health impacts of the COVID-19 pandemic requires the consideration of mobility networks. To this aim, we propose to augment spatio-temporal point process models with mobility network covariates. We show how the resulting model can be employed to predict contagion patterns and to help in important decisions such as the distribution of vaccines. The application of the proposed methodology to 27 European countries shows that human mobility, along with vaccine doses and government policies, are significant predictors of the number of new COVID-19 reported infections and are therefore key variables for decision-making. [ABSTRACT FROM AUTHOR]

Mobile phones contain a wealth of private information, so we try to keep them secure. We provide large-scale evidence that the psychological profiles of individuals and their relations with their peers can be predicted from seemingly anonymous communication traces–calling and texting logs that service providers routinely collect. Based on two extensive longitudinal studies containing more than 900 college students, we use point process modeling to describe communication patterns. We automatically predict the peer relationship type and temporal dynamics, and assess user personality based on the modeling. For some personality traits, the results are comparable to the gold-standard performances obtained from survey self-report data. Findings illustrate how information usually residing outside the control of individuals can be used to reconstruct sensitive information.

Hawkes process is a class of self-exciting point processes with clustering effect whose jump rate relies on their entire past history. This process is usually defined as a continuous-time setting and has been widely applied in several fields, including insurance, finance, queueing theory, and statistics. The Hawkes model is generally non-Markovian because the future development of a self-exciting point process is determined by the timing of past events. However, it can be Markovian in special cases such as when the exciting function is an exponential function or a sum of exponential functions. Difficulty arises when the exciting function is not an exponential function or a sum of exponentials, in which case the process can be non-Markovian. The inverse Markovian case for Hawkes processes was introduced by Seol (Stat. Probab. Lett. 155:108580, 2019) who studied some asymptotic behaviors. An extended version of the inverse Markovian Hawkes process was also studied by Seol (J. Korean Math. Soc. 58(4):819–833, 2021). In the current work, we propose a class of Markovian self-exciting processes that interpolates between the Hawkes process and the inverse Hawkes process. We derived limit theorems for the newly considered class of Markovian self-exciting processes. In particular, we established both the law of large numbers (LLN) and central limit theorems (CLT) with some key results. [ABSTRACT FROM AUTHOR]

In this paper we provide an expansion formula for Hawkes processes which involves the addition of jumps at deterministic times to the Hawkes process in the spirit of the well-known integration by parts formula (or more precisely the Mecke formula) for Poisson functional. Our approach allows us to provide an expansion of the premium of a class of cyber insurance derivatives (such as reinsurance contracts including generalized Stop-Loss contracts) or risk management instruments (like Expected Shortfall) in terms of so-called shifted Hawkes processes. From the actuarial point of view, these processes can be seen as "stressed" scenarios. Our expansion formula for Hawkes processes enables us to provide lower and upper bounds on the premium (or the risk evaluation) of such cyber contracts and to quantify the surplus of premium compared to the standard modeling with a homogeneous Poisson process. [ABSTRACT FROM AUTHOR]

We consider the asset price as the weak solution to a stochastic differential equation driven by both a Brownian motion and the counting process martingale whose predictable compensator follows shot-noise and Hawkes processes. In this framework, we discuss the Esscher martingale measure where the conditions for its existence are detailed. This generalizes certain relationships not yet encountered in the literature. [ABSTRACT FROM AUTHOR]

This article describes the limiting distribution of the extremes of observations that arrive in clusters. We start by studying the tail behaviour of an individual cluster, and then we apply the developed theory to determine the limiting distribution of $\max\{X_j\,:\, j=0,\ldots, K(t)\}$ , where K (t) is the number of independent and identically distributed observations $(X_j)$ arriving up to the time t according to a general marked renewal cluster process. The results are illustrated in the context of some commonly used Poisson cluster models such as the marked Hawkes process. [ABSTRACT FROM AUTHOR]