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APR volume 55 issue 1 Cover and Back matter APR第55卷第1期封面和封底
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-02-13 DOI: 10.1017/apr.2022.68
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引用次数: 0
APR volume 55 issue 1 Cover and Front matter APR第55卷第1期封面和封面问题
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-02-13 DOI: 10.1017/apr.2022.67
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引用次数: 0
PDE for the joint law of the pair of a continuous diffusion and its running maximum PDE为连续扩散对及其运行最大值的联合律
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-01-06 DOI: 10.1017/apr.2022.76
L. Coutin, M. Pontier
{"title":"PDE for the joint law of the pair of a continuous diffusion and its running maximum","authors":"L. Coutin, M. Pontier","doi":"10.1017/apr.2022.76","DOIUrl":"https://doi.org/10.1017/apr.2022.76","url":null,"abstract":"\u0000\t <jats:p>Let <jats:italic>X</jats:italic> be a <jats:italic>d</jats:italic>-dimensional diffusion and <jats:italic>M</jats:italic> the running supremum of its first component. In this paper, we show that for any <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0001867822000763_inline1.png\" />\u0000\t\t<jats:tex-math>\u0000$t>0,$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> the density (with respect to the <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0001867822000763_inline2.png\" />\u0000\t\t<jats:tex-math>\u0000$(d+1)$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>-dimensional Lebesgue measure) of the pair <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0001867822000763_inline3.png\" />\u0000\t\t<jats:tex-math>\u0000$big(M_t,X_tbig)$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> is a weak solution of a Fokker–Planck partial differential equation on the closed set <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0001867822000763_inline4.png\" />\u0000\t\t<jats:tex-math>\u0000$big{(m,x)in mathbb{R}^{d+1},,{mgeq x^1}big},$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> using an integral expansion of this density.</jats:p>","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45018909","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
APR volume 54 issue 4 Cover and Front matter APR第54卷第4期封面和封面
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2022-11-07 DOI: 10.1017/apr.2022.65
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引用次数: 0
APR volume 54 issue 4 Cover and Back matter APR第54卷第4期封面和封底
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2022-11-07 DOI: 10.1017/apr.2022.66
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引用次数: 0
APR volume 54 issue 3 Cover and Front matter APR第54卷第3期封面和封面
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2022-09-01 DOI: 10.1017/apr.2022.44
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引用次数: 0
A functional central limit theorem for SI processes on configuration model graphs 配置模型图上SI过程的一个函数中心极限定理
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2022-09-01 DOI: 10.1017/apr.2022.52
Wasiur R. KhudaBukhsh, Casper Woroszyło, G. Rempała, H. Koeppl
{"title":"A functional central limit theorem for SI processes on configuration model graphs","authors":"Wasiur R. KhudaBukhsh, Casper Woroszyło, G. Rempała, H. Koeppl","doi":"10.1017/apr.2022.52","DOIUrl":"https://doi.org/10.1017/apr.2022.52","url":null,"abstract":"Abstract We study a stochastic compartmental susceptible–infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph vertices into two compartments, namely, S and I, denoting susceptible and infected vertices, respectively. In addition to the sizes of these two compartments, we keep track of the counts of SI-edges (those connecting a susceptible and an infected vertex) and SS-edges (those connecting two susceptible vertices). We describe the dynamical process in terms of these counts and present a functional central limit theorem (FCLT) for them as the number of vertices in the random graph grows to infinity. The FCLT asserts that the counts, when appropriately scaled, converge weakly to a continuous Gaussian vector semimartingale process in the space of vector-valued càdlàg functions endowed with the Skorokhod topology. We discuss applications of the FCLT in percolation theory and in modelling the spread of computer viruses. We also provide simulation results illustrating the FCLT for some common degree distributions.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42366140","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
APR volume 54 issue 3 Cover and Back matter APR第54卷第3期封面和封底
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2022-09-01 DOI: 10.1017/apr.2022.45
{"title":"APR volume 54 issue 3 Cover and Back matter","authors":"","doi":"10.1017/apr.2022.45","DOIUrl":"https://doi.org/10.1017/apr.2022.45","url":null,"abstract":"","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45659897","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
Critical cluster cascades 关键集群级联
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2022-08-17 DOI: 10.1017/apr.2022.26
Matthias Kirchner
{"title":"Critical cluster cascades","authors":"Matthias Kirchner","doi":"10.1017/apr.2022.26","DOIUrl":"https://doi.org/10.1017/apr.2022.26","url":null,"abstract":"Abstract We consider a sequence of Poisson cluster point processes on \u0000$mathbb{R}^d$\u0000 : at step \u0000$ninmathbb{N}_0$\u0000 of the construction, the cluster centers have intensity \u0000$c/(n+1)$\u0000 for some \u0000$c>0$\u0000 , and each cluster consists of the particles of a branching random walk up to generation n—generated by a point process with mean 1. We show that this ‘critical cluster cascade’ converges weakly, and that either the limit point process equals the void process (extinction), or it has the same intensity c as the critical cluster cascade (persistence). We obtain persistence if and only if the Palm version of the outgrown critical branching random walk is locally almost surely finite. This result allows us to give numerous examples for persistent critical cluster cascades.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47415286","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
Construction of aggregation paradoxes through load-sharing models 基于负荷分担模型的聚合悖论构建
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2022-08-08 DOI: 10.1017/apr.2022.17
Emilio De Santis, F. Spizzichino
{"title":"Construction of aggregation paradoxes through load-sharing models","authors":"Emilio De Santis, F. Spizzichino","doi":"10.1017/apr.2022.17","DOIUrl":"https://doi.org/10.1017/apr.2022.17","url":null,"abstract":"Abstract We show that load-sharing models (a very special class of multivariate probability models for nonnegative random variables) can be used to obtain basic results about a multivariate extension of stochastic precedence and related paradoxes. Such results can be applied in several different fields. In particular, applications of them can be developed in the context of paradoxes which arise in voting theory. Also, an application to the notion of probability signature may be of interest, in the field of systems reliability.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47547784","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
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