Journal of Applied Probability最新文献

{"title":"Non-hyperuniformity of Gibbs point processes with short-range interactions","authors":"David Dereudre, Daniela Flimmel","doi":"10.1017/jpr.2024.21","DOIUrl":"https://doi.org/10.1017/jpr.2024.21","url":null,"abstract":"We investigate the hyperuniformity of marked Gibbs point processes that have weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Various stability and range assumptions are imposed on the Papangelou intensity in order to prove that the resulting point process is not hyperuniform. The scope of our results covers many frequently used models, including Gibbs point processes with a superstable, lower-regular, integrable pair potential, as well as the Widom–Rowlinson model with random radii and Gibbs point processes with interactions based on Voronoi tessellations and nearest-neighbour graphs.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"190 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141885314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the speed of convergence of discrete Pickands constants to continuous ones","authors":"Krzysztof Bisewski, Grigori Jasnovidov","doi":"10.1017/jpr.2024.37","DOIUrl":"https://doi.org/10.1017/jpr.2024.37","url":null,"abstract":"In this manuscript, we address open questions raised by Dieker and Yakir (2014), who proposed a novel method of estimating (discrete) Pickands constants <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000378_inline1.png\"/> <jats:tex-math> $mathcal{H}^delta_alpha$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> using a family of estimators <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000378_inline2.png\"/> <jats:tex-math> $xi^delta_alpha(T)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000378_inline3.png\"/> <jats:tex-math> $T>0$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000378_inline4.png\"/> <jats:tex-math> $alphain(0,2]$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is the Hurst parameter, and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000378_inline5.png\"/> <jats:tex-math> $deltageq0$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is the step size of the regular discretization grid. We derive an upper bound for the discretization error <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000378_inline6.png\"/> <jats:tex-math> $mathcal{H}_alpha^0 - mathcal{H}_alpha^delta$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, whose rate of convergence agrees with Conjecture 1 of Dieker and Yakir (2014) in the case <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000378_inline7.png\"/> <jats:tex-math> $alphain(0,1]$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and agrees up to logarithmic terms for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000378_inline8.png\"/> <jats:tex-math> $alphain(1,2)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. Moreover, we show that all moments of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000378_inline9.png\"/> <jats:tex-math> $xi_alpha^delta(T)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> are uniformly bounded and the bias of the estimator decays no slower than <jats:inline-formula> <jats:alte","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Persistence of spectral projections for stochastic operators on large tensor products","authors":"Robert S. Mackay","doi":"10.1017/jpr.2024.34","DOIUrl":"https://doi.org/10.1017/jpr.2024.34","url":null,"abstract":"<p>It is proved that for families of stochastic operators on a countable tensor product, depending smoothly on parameters, any spectral projection persists smoothly, where smoothness is defined using norms based on ideas of Dobrushin. A rigorous perturbation theory for families of stochastic operators with spectral gap is thereby created. It is illustrated by deriving an effective slow two-state dynamics for a three-state probabilistic cellular automaton.</p>","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"43 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141257973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bivariate tempered space-fractional Poisson process and shock models","authors":"Ritik Soni, Ashok Kumar Pathak, Antonio Di Crescenzo, Alessandra Meoli","doi":"10.1017/jpr.2024.30","DOIUrl":"https://doi.org/10.1017/jpr.2024.30","url":null,"abstract":"We introduce a bivariate tempered space-fractional Poisson process (BTSFPP) by time-changing the bivariate Poisson process with an independent tempered <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000305_inline1.png\"/> <jats:tex-math> $alpha$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-stable subordinator. We study its distributional properties and its connection to differential equations. The Lévy measure for the BTSFPP is also derived. A bivariate competing risks and shock model based on the BTSFPP for predicting the failure times of items that undergo two random shocks is also explored. The system is supposed to break when the sum of two types of shock reaches a certain random threshold. Various results related to reliability, such as reliability function, hazard rates, failure density, and the probability that failure occurs due to a certain type of shock, are studied. We show that for a general Lévy subordinator, the failure time of the system is exponentially distributed with mean depending on the Laplace exponent of the Lévy subordinator when the threshold has a geometric distribution. Some special cases and several typical examples are also demonstrated.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"43 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometric random intersection graphs with general connection probabilities","authors":"Maria Deijfen, Riccardo Michielan","doi":"10.1017/jpr.2024.18","DOIUrl":"https://doi.org/10.1017/jpr.2024.18","url":null,"abstract":"Let &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline1.png\"/&gt; &lt;jats:tex-math&gt; $mathcal{V}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline2.png\"/&gt; &lt;jats:tex-math&gt; $mathcal{U}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; be the point sets of two independent homogeneous Poisson processes on &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline3.png\"/&gt; &lt;jats:tex-math&gt; $mathbb{R}^d$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. A graph &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline4.png\"/&gt; &lt;jats:tex-math&gt; $mathcal{G}_mathcal{V}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; with vertex set &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline5.png\"/&gt; &lt;jats:tex-math&gt; $mathcal{V}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is constructed by first connecting pairs of points (&lt;jats:italic&gt;v&lt;/jats:italic&gt;, &lt;jats:italic&gt;u&lt;/jats:italic&gt;) with &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline6.png\"/&gt; &lt;jats:tex-math&gt; $vinmathcal{V}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline7.png\"/&gt; &lt;jats:tex-math&gt; $uinmathcal{U}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; independently with probability &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline8.png\"/&gt; &lt;jats:tex-math&gt; $g(v-u)$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, where &lt;jats:italic&gt;g&lt;/jats:italic&gt; is a non-increasing radial function, and then connecting two points &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline9.png\"/&gt; &lt;jats:tex-math&gt; $v_1,v_2inmathcal{V}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; if and only if they have a joint neighbor &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline10.png\"/&gt; &lt;jats:tex-math&gt; $uinmathcal{U}$ &lt;/jats:tex-math&gt; &lt;/jats:alternati","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"54 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Depths in random recursive metric spaces","authors":"Colin Desmarais","doi":"10.1017/jpr.2024.32","DOIUrl":"https://doi.org/10.1017/jpr.2024.32","url":null,"abstract":"As a generalization of random recursive trees and preferential attachment trees, we consider random recursive metric spaces. These spaces are constructed from random blocks, each a metric space equipped with a probability measure, containing a labelled point called a hook, and assigned a weight. Random recursive metric spaces are equipped with a probability measure made up of a weighted sum of the probability measures assigned to its constituent blocks. At each step in the growth of a random recursive metric space, a point called a latch is chosen at random according to the equipped probability measure, and a new block is chosen at random and attached to the space by joining together the latch and the hook of the block. We use martingale theory to prove a law of large numbers and a central limit theorem for the insertion depth, the distance from the master hook to the latch chosen. We also apply our results to further generalizations of random trees, hooking networks, and continuous spaces constructed from line segments.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"7 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multivariate regularly varying insurance and financial risks in multidimensional risk models","authors":"Ming Cheng, Dimitrios G. Konstantinides, Dingcheng Wang","doi":"10.1017/jpr.2024.23","DOIUrl":"https://doi.org/10.1017/jpr.2024.23","url":null,"abstract":"Multivariate regular variation is a key concept that has been applied in finance, insurance, and risk management. This paper proposes a new dependence assumption via a framework of multivariate regular variation. Under the condition that financial and insurance risks satisfy our assumption, we conduct asymptotic analyses for multidimensional ruin probabilities in the discrete-time and continuous-time cases. Also, we present a two-dimensional numerical example satisfying our assumption, through which we show the accuracy of the asymptotic result for the discrete-time multidimensional insurance risk model.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"16 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Perturbation analysis for continuous-time Markov chains in a weak sense","authors":"Na Lin, Yuanyuan Liu","doi":"10.1017/jpr.2024.20","DOIUrl":"https://doi.org/10.1017/jpr.2024.20","url":null,"abstract":"By the technique of augmented truncations, we obtain the perturbation bounds on the distance of the finite-time state distributions of two continuous-time Markov chains (CTMCs) in a type of weaker norm than the <jats:italic>V</jats:italic>-norm. We derive the estimates for strongly and exponentially ergodic CTMCs. In particular, we apply these results to get the bounds for CTMCs satisfying Doeblin or stochastically monotone conditions. Some examples are presented to illustrate the limitation of the <jats:italic>V</jats:italic>-norm in perturbation analysis and to show the quality of the weak norm.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"41 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Branching processes in nearly degenerate varying environment","authors":"Péter Kevei, Kata Kubatovics","doi":"10.1017/jpr.2024.15","DOIUrl":"https://doi.org/10.1017/jpr.2024.15","url":null,"abstract":"We investigate branching processes in varying environment, for which <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000159_inline1.png\"/> <jats:tex-math> $overline{f}_n to 1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000159_inline2.png\"/> <jats:tex-math> $sum_{n=1}^infty (1-overline{f}_n)_+ = infty$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000159_inline3.png\"/> <jats:tex-math> $sum_{n=1}^infty (overline{f}_n - 1)_+ &lt; infty$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000159_inline4.png\"/> <jats:tex-math> $overline{f}_n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> stands for the offspring mean in generation <jats:italic>n</jats:italic>. Since subcritical regimes dominate, such processes die out almost surely, therefore to obtain a nontrivial limit we consider two scenarios: conditioning on nonextinction, and adding immigration. In both cases we show that the process converges in distribution without normalization to a nondegenerate compound-Poisson limit law. The proofs rely on the shape function technique, worked out by Kersting (2020).","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"15 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A remark on exact simulation of tempered stable Ornstein–Uhlenbeck processes","authors":"Takuji Arai, Yuto Imai","doi":"10.1017/jpr.2024.17","DOIUrl":"https://doi.org/10.1017/jpr.2024.17","url":null,"abstract":"Qu, Dassios, and Zhao (2021) suggested an exact simulation method for tempered stable Ornstein–Uhlenbeck processes, but their algorithms contain some errors. This short note aims to correct their algorithms and conduct some numerical experiments.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"8 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}