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Weak convergence of the extremes of branching Lévy processes with regularly varying tails 具有规则变化尾的分支lsamvy过程的极端的弱收敛性
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2023-12-06 DOI: 10.1017/jpr.2023.103
Yan-xia Ren, Renming Song, Rui Zhang
{"title":"Weak convergence of the extremes of branching Lévy processes with regularly varying tails","authors":"Yan-xia Ren, Renming Song, Rui Zhang","doi":"10.1017/jpr.2023.103","DOIUrl":"https://doi.org/10.1017/jpr.2023.103","url":null,"abstract":"We study the weak convergence of the extremes of supercritical branching Lévy processes <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223001031_inline1.png\" /> <jats:tex-math> ${mathbb{X}_t, t ge0}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> whose spatial motions are Lévy processes with regularly varying tails. The result is drastically different from the case of branching Brownian motions. We prove that, when properly renormalized, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223001031_inline2.png\" /> <jats:tex-math> $mathbb{X}_t$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> converges weakly. As a consequence, we obtain a limit theorem for the order statistics of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223001031_inline3.png\" /> <jats:tex-math> $mathbb{X}_t$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524156","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: 1
Speed of extinction for continuous-state branching processes in a weakly subcritical Lévy environment 弱亚临界lims环境下连续状态分支过程的消光速度
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2023-12-01 DOI: 10.1017/jpr.2023.92
Natalia Cardona-Tobón, Juan Carlos Pardo
{"title":"Speed of extinction for continuous-state branching processes in a weakly subcritical Lévy environment","authors":"Natalia Cardona-Tobón, Juan Carlos Pardo","doi":"10.1017/jpr.2023.92","DOIUrl":"https://doi.org/10.1017/jpr.2023.92","url":null,"abstract":"We continue with the systematic study of the speed of extinction of continuous-state branching processes in Lévy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime under the assumption that the branching mechanism is regularly varying. We extend recent results of Li and Xu (2018) and Palau et al. (2016), where it is assumed that the branching mechanism is stable, and complement the recent articles of Bansaye et al. (2021) and Cardona-Tobón and Pardo (2021), where the critical and the strongly and intermediate subcritical cases were treated, respectively. Our methodology combines a path analysis of the branching process together with its Lévy environment, fluctuation theory for Lévy processes, and the asymptotic behaviour of exponential functionals of Lévy processes. Our approach is inspired by the last two previously cited papers, and by Afanasyev et al. (2012), where the analogue was obtained.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524155","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: 1
JPR volume 60 issue 4 Cover and Back matter JPR 第 60 卷第 4 期封面和封底
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2023-12-01 DOI: 10.1017/jpr.2023.56
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引用次数: 0
JPR volume 60 issue 4 Cover and Front matter JPR 第 60 卷第 4 期 封面和封底
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2023-12-01 DOI: 10.1017/jpr.2023.55
{"title":"JPR volume 60 issue 4 Cover and Front matter","authors":"","doi":"10.1017/jpr.2023.55","DOIUrl":"https://doi.org/10.1017/jpr.2023.55","url":null,"abstract":"","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139012773","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
Daryl John Daley, 4 April 1939 – 16 April 2023 An internationally acclaimed researcher in applied probability and a gentleman of great kindness 达里尔-约翰-戴利，1939 年 4 月 4 日 - 2023 年 4 月 16 日 他是国际知名的应用概率研究员，也是一位非常和蔼可亲的绅士。
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2023-12-01 DOI: 10.1017/jpr.2023.90
Peter G. Taylor
{"title":"Daryl John Daley, 4 April 1939 – 16 April 2023 An internationally acclaimed researcher in applied probability and a gentleman of great kindness","authors":"Peter G. Taylor","doi":"10.1017/jpr.2023.90","DOIUrl":"https://doi.org/10.1017/jpr.2023.90","url":null,"abstract":"","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139022048","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
Local convergence of critical Galton–Watson trees 临界高尔顿-沃森树的局部收敛性
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2023-11-30 DOI: 10.1017/jpr.2023.83
Aymen Bouaziz
{"title":"Local convergence of critical Galton–Watson trees","authors":"Aymen Bouaziz","doi":"10.1017/jpr.2023.83","DOIUrl":"https://doi.org/10.1017/jpr.2023.83","url":null,"abstract":"We study the local convergence of critical Galton–Watson trees under various conditionings. We give a sufficient condition, which serves to cover all previous known results, for the convergence in distribution of a conditioned Galton–Watson tree to Kesten’s tree. We also propose a new proof to give the limit in distribution of a critical Galton–Watson tree, with finite support, conditioned on having a large width.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524152","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
Dynamics of information networks 信息网络动力学
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2023-11-30 DOI: 10.1017/jpr.2023.91
Andrei Sontag, Tim Rogers, Christian A Yates
{"title":"Dynamics of information networks","authors":"Andrei Sontag, Tim Rogers, Christian A Yates","doi":"10.1017/jpr.2023.91","DOIUrl":"https://doi.org/10.1017/jpr.2023.91","url":null,"abstract":"We explore a simple model of network dynamics which has previously been applied to the study of information flow in the context of epidemic spreading. A random rooted network is constructed that evolves according to the following rule: at a constant rate, pairs of nodes (<jats:italic>i</jats:italic>, <jats:italic>j</jats:italic>) are randomly chosen to interact, with an edge drawn from <jats:italic>i</jats:italic> to <jats:italic>j</jats:italic> (and any other out-edge from <jats:italic>i</jats:italic> deleted) if <jats:italic>j</jats:italic> is strictly closer to the root with respect to graph distance. We characterise the dynamics of this random network in the limit of large size, showing that it instantaneously forms a tree with long branches that immediately collapse to depth two, then it slowly rearranges itself to a star-like configuration. This curious behaviour has consequences for the study of the epidemic models in which this information network was first proposed.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524207","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
Characteristics of the switch process and geometric divisibility 开关过程的特点及几何可分性
4区 数学
Journal of Applied Probability Pub Date : 2023-11-06 DOI: 10.1017/jpr.2023.81
Henrik Bengtsson
{"title":"Characteristics of the switch process and geometric divisibility","authors":"Henrik Bengtsson","doi":"10.1017/jpr.2023.81","DOIUrl":"https://doi.org/10.1017/jpr.2023.81","url":null,"abstract":"Abstract The switch process alternates independently between 1 and $-1$ , with the first switch to 1 occurring at the origin. The expected value function of this process is defined uniquely by the distribution of switching times. The relation between the two is implicitly described through the Laplace transform, which is difficult to use for determining if a given function is the expected value function of some switch process. We derive an explicit relation under the assumption of monotonicity of the expected value function. It is shown that geometric divisible switching time distributions correspond to a non-negative decreasing expected value function. Moreover, an explicit relation between the expected value of a switch process and the autocovariance function of the switch process stationary counterpart is obtained, leading to a new interpretation of the classical Pólya criterion for positive-definiteness.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135635344","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
Tessellation-valued processes that are generated by cell division 由细胞分裂产生的有镶嵌价值的过程
4区 数学
Journal of Applied Probability Pub Date : 2023-11-01 DOI: 10.1017/jpr.2023.66
Servet Martínez, Werner Nagel
{"title":"Tessellation-valued processes that are generated by cell division","authors":"Servet Martínez, Werner Nagel","doi":"10.1017/jpr.2023.66","DOIUrl":"https://doi.org/10.1017/jpr.2023.66","url":null,"abstract":"Abstract Processes of random tessellations of the Euclidean space $mathbb{R}^d$ , $dgeq 1$ , are considered that are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until their division and by the laws for the random hyperplanes that divide the cells at the end of their life times. The STIT (STable with respect to ITerations) tessellation processes are a reference model. In the present paper a generalization concerning the life time distributions is introduced, a sufficient condition for the existence of such cell division tessellation processes is provided, and a construction is described. In particular, for the case that the random dividing hyperplanes have a Mondrian distribution—which means that all cells of the tessellations are cuboids—it is shown that the intrinsic volumes, except the Euler characteristic, can be used as the parameter for the exponential life time distribution of the cells.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135221049","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: 2
Trajectory fitting estimation for reflected stochastic linear differential equations of a large signal 大信号反射随机线性微分方程的轨迹拟合估计
4区 数学
Journal of Applied Probability Pub Date : 2023-10-31 DOI: 10.1017/jpr.2023.78
Xuekang Zhang, Huisheng Shu
{"title":"Trajectory fitting estimation for reflected stochastic linear differential equations of a large signal","authors":"Xuekang Zhang, Huisheng Shu","doi":"10.1017/jpr.2023.78","DOIUrl":"https://doi.org/10.1017/jpr.2023.78","url":null,"abstract":"Abstract In this paper we study the drift parameter estimation for reflected stochastic linear differential equations of a large signal. We discuss the consistency and asymptotic distributions of trajectory fitting estimator (TFE).","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135862988","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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