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Non-hyperuniformity of Gibbs point processes with short-range interactions 具有短程相互作用的吉布斯点过程的非超均匀性
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-08-02 DOI: 10.1017/jpr.2024.21
David Dereudre, Daniela Flimmel
{"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":null,"pages":null},"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}
引用次数: 0
On the speed of convergence of discrete Pickands constants to continuous ones 论离散皮康兹常数向连续常数的收敛速度
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-07-31 DOI: 10.1017/jpr.2024.37
Krzysztof Bisewski, Grigori Jasnovidov
{"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> $T&gt;0$ </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":null,"pages":null},"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}
引用次数: 0
Persistence of spectral projections for stochastic operators on large tensor products 大张量乘上随机算子谱投影的持久性
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-06-03 DOI: 10.1017/jpr.2024.34
Robert S. Mackay
{"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":null,"pages":null},"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}
引用次数: 0
(Almost) complete characterization of the stability of a discrete-time Hawkes process with inhibition and memory of length two (具有抑制和长度为 2 的记忆的离散时间霍克斯过程稳定性的(几乎)完整表征
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-05-24 DOI: 10.1017/jpr.2024.28
Manon Costa, Pascal Maillard, Anthony Muraro
{"title":"(Almost) complete characterization of the stability of a discrete-time Hawkes process with inhibition and memory of length two","authors":"Manon Costa, Pascal Maillard, Anthony Muraro","doi":"10.1017/jpr.2024.28","DOIUrl":"https://doi.org/10.1017/jpr.2024.28","url":null,"abstract":"\u0000 We consider a Poisson autoregressive process whose parameters depend on the past of the trajectory. We allow these parameters to take negative values, modelling inhibition. More precisely, the model is the stochastic process \u0000 \u0000 \u0000 \u0000$(X_n)_{nge0}$\u0000\u0000 \u0000 with parameters \u0000 \u0000 \u0000 \u0000$a_1,ldots,a_p in mathbb{R}$\u0000\u0000 \u0000 , \u0000 \u0000 \u0000 \u0000$pinmathbb{N}$\u0000\u0000 \u0000 , and \u0000 \u0000 \u0000 \u0000$lambda ge 0$\u0000\u0000 \u0000 , such that, for all \u0000 \u0000 \u0000 \u0000$nge p$\u0000\u0000 \u0000 , conditioned on \u0000 \u0000 \u0000 \u0000$X_0,ldots,X_{n-1}$\u0000\u0000 \u0000 , \u0000 \u0000 \u0000 \u0000$X_n$\u0000\u0000 \u0000 is Poisson distributed with parameter \u0000 \u0000 \u0000 \u0000$(a_1 X_{n-1} + cdots + a_p X_{n-p} + lambda)_+$\u0000\u0000 \u0000 . This process can be regarded as a discrete-time Hawkes process with inhibition and a memory of length p. In this paper we initiate the study of necessary and sufficient conditions of stability for these processes, which seems to be a hard problem in general. We consider specifically the case \u0000 \u0000 \u0000 \u0000$p = 2$\u0000\u0000 \u0000 , for which we are able to classify the asymptotic behavior of the process for the whole range of parameters, except for boundary cases. In particular, we show that the process remains stochastically bounded whenever the solution to the linear recurrence equation \u0000 \u0000 \u0000 \u0000$x_n = a_1x_{n-1} + a_2x_{n-2} + lambda$\u0000\u0000 \u0000 remains bounded, but the converse is not true. Furthermore, the criterion for stochastic boundedness is not symmetric in \u0000 \u0000 \u0000 \u0000$a_1$\u0000\u0000 \u0000 and \u0000 \u0000 \u0000 \u0000$a_2$\u0000\u0000 \u0000 , in contrast to the case of non-negative parameters, illustrating the complex effects of inhibition.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141100378","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}
引用次数: 0
Bivariate tempered space-fractional Poisson process and shock models 双变量节制空间分数泊松过程和冲击模型
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-05-23 DOI: 10.1017/jpr.2024.30
Ritik Soni, Ashok Kumar Pathak, Antonio Di Crescenzo, Alessandra Meoli
{"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":null,"pages":null},"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}
引用次数: 0
Geometric random intersection graphs with general connection probabilities 具有一般连接概率的几何随机相交图
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-05-22 DOI: 10.1017/jpr.2024.18
Maria Deijfen, Riccardo Michielan
{"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 <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline1.png\"/> <jats:tex-math> $mathcal{V}$ </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=\"S0021900224000184_inline2.png\"/> <jats:tex-math> $mathcal{U}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be the point sets of two independent homogeneous Poisson processes on <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline3.png\"/> <jats:tex-math> $mathbb{R}^d$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. A graph <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline4.png\"/> <jats:tex-math> $mathcal{G}_mathcal{V}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with vertex set <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline5.png\"/> <jats:tex-math> $mathcal{V}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is constructed by first connecting pairs of points (<jats:italic>v</jats:italic>, <jats:italic>u</jats:italic>) with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline6.png\"/> <jats:tex-math> $vinmathcal{V}$ </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=\"S0021900224000184_inline7.png\"/> <jats:tex-math> $uinmathcal{U}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> independently with probability <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline8.png\"/> <jats:tex-math> $g(v-u)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:italic>g</jats:italic> is a non-increasing radial function, and then connecting two points <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline9.png\"/> <jats:tex-math> $v_1,v_2inmathcal{V}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> if and only if they have a joint neighbor <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000184_inline10.png\"/> <jats:tex-math> $uinmathcal{U}$ </jats:tex-math> </jats:alternati","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"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}
引用次数: 0
Depths in random recursive metric spaces 随机递归度量空间中的深度
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-05-20 DOI: 10.1017/jpr.2024.32
Colin Desmarais
{"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":null,"pages":null},"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}
引用次数: 0
Series expansions for random disc-polygons in smooth plane convex bodies 光滑平面凸体中随机圆盘多边形的序列展开
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-05-16 DOI: 10.1017/jpr.2024.27
F. Fodor, Nicolás A. Montenegro Pinzón
{"title":"Series expansions for random disc-polygons in smooth plane convex bodies","authors":"F. Fodor, Nicolás A. Montenegro Pinzón","doi":"10.1017/jpr.2024.27","DOIUrl":"https://doi.org/10.1017/jpr.2024.27","url":null,"abstract":"\u0000 We establish power-series expansions for the asymptotic expectations of the vertex number and missed area of random disc-polygons in planar convex bodies with \u0000 \u0000 \u0000 \u0000$C^{k+1}_+$\u0000\u0000 \u0000 -smooth boundaries. These results extend asymptotic formulas proved in Fodor et al. (2014).","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140968604","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}
引用次数: 0
Multivariate regularly varying insurance and financial risks in multidimensional risk models 多维风险模型中的多变量有规律变化的保险和金融风险
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-05-13 DOI: 10.1017/jpr.2024.23
Ming Cheng, Dimitrios G. Konstantinides, Dingcheng Wang
{"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":null,"pages":null},"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}
引用次数: 0
Perturbation analysis for continuous-time Markov chains in a weak sense 弱意义上连续时间马尔可夫链的扰动分析
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-05-13 DOI: 10.1017/jpr.2024.20
Na Lin, Yuanyuan Liu
{"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":null,"pages":null},"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}
引用次数: 0
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