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Theory of Probability and its Applications最新文献

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Moment Asymptotics of Population Size of Particles at Vertices for a Supercritical Branching Random Walk on a Periodic Graph 周期图上超临界分支随机漫步的顶点粒子总体大小的矩渐近性
4区 数学
Theory of Probability and its Applications Pub Date : 2023-08-01 DOI: 10.1137/s0040585x97t991386
M. V. Platonova, K. S. Ryadovkin
{"title":"Moment Asymptotics of Population Size of Particles at Vertices for a Supercritical Branching Random Walk on a Periodic Graph","authors":"M. V. Platonova, K. S. Ryadovkin","doi":"10.1137/s0040585x97t991386","DOIUrl":"https://doi.org/10.1137/s0040585x97t991386","url":null,"abstract":"We consider a continuous-time supercritical symmetric branching random walk on a multidimensional graph with periodic particle generation sources. A logarithmic asymptotic formula is obtained for the moments of population sizes of particles at each vertex of the graph as ${ttoinfty}$.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136021779","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 Sum of Gaussian Martingale and an Independent Fractional Brownian Motion 高斯鞅与独立分数布朗运动的和
4区 数学
Theory of Probability and its Applications Pub Date : 2023-08-01 DOI: 10.1137/s0040585x97t991441
R. Belfadli, M. Chadad, M. Erraoui
{"title":"On the Sum of Gaussian Martingale and an Independent Fractional Brownian Motion","authors":"R. Belfadli, M. Chadad, M. Erraoui","doi":"10.1137/s0040585x97t991441","DOIUrl":"https://doi.org/10.1137/s0040585x97t991441","url":null,"abstract":"In the same context as in the seminal paper [P. Cheridito, Bernoulli, 7 (2001), pp. 913--934], we are concerned with the semimartingale property of the sum of some Gaussian martingale and an independent fractional Brownian motion with Hurst parameter $H in (0,1)$. At the same time, we emphasize that the Markov property is lost even if the martingale owns it.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136021781","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 of Fractional Brownian Motions and Strong Local Nondeterminism of Bifractional Brownian Motions on Balls and Spheres 球和球上分数布朗运动的级数展开式和双分数布朗运动的强局部不确定性
4区 数学
Theory of Probability and its Applications Pub Date : 2023-05-01 DOI: 10.1137/s0040585x97t991301
T. Lu, C. Ma, F. Wang
{"title":"Series Expansions of Fractional Brownian Motions and Strong Local Nondeterminism of Bifractional Brownian Motions on Balls and Spheres","authors":"T. Lu, C. Ma, F. Wang","doi":"10.1137/s0040585x97t991301","DOIUrl":"https://doi.org/10.1137/s0040585x97t991301","url":null,"abstract":"This paper provides series expansions for fractional Brownian motions on the unit ball and the unit sphere by means of ultraspherical polynomials and spherical harmonics. It establishes the property of strong local nondeterminism of isotropic Gaussian random fields on the unit sphere and that of fractional and bifractional Brownian motions on the unit ball and the unit sphere.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135658638","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
Optimal Information Usage in Binary Sequential Hypothesis Testing 二值序列假设检验中的最优信息利用
4区 数学
Theory of Probability and its Applications Pub Date : 2023-05-01 DOI: 10.1137/s0040585x97t991295
M. Dörpinghaus, I. Neri, É. Roldán, F. Jülicher
{"title":"Optimal Information Usage in Binary Sequential Hypothesis Testing","authors":"M. Dörpinghaus, I. Neri, É. Roldán, F. Jülicher","doi":"10.1137/s0040585x97t991295","DOIUrl":"https://doi.org/10.1137/s0040585x97t991295","url":null,"abstract":"An interesting question is whether an information theoretic interpretation can be given of optimal algorithms in sequential hypothesis testing. We prove that for the binary sequential probability ratio test of a continuous observation process, the mutual information between the observation process up to the decision time and the actual hypothesis conditioned on the decision variable is equal to zero. This result can be interpreted as an optimal usage of the information on the hypothesis available in the observations by the sequential probability ratio test. As a consequence, the mutual information between the random decision time of the sequential probability ratio test and the actual hypothesis conditioned on the decision variable is also equal to zero.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136273940","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
Abstracts of Talks Given at the 7th International Conference on Stochastic Methods, II 第七届国际随机方法会议报告摘要，2
4区 数学
Theory of Probability and its Applications Pub Date : 2023-05-01 DOI: 10.1137/s0040585x97t991337
A. N. Shiryaev, I. V. Pavlov
{"title":"Abstracts of Talks Given at the 7th International Conference on Stochastic Methods, II","authors":"A. N. Shiryaev, I. V. Pavlov","doi":"10.1137/s0040585x97t991337","DOIUrl":"https://doi.org/10.1137/s0040585x97t991337","url":null,"abstract":"This is the second installment of a two-part article presenting abstracts of talks given at the 7th International Conference on Stochastic Methods (ICSM-7), held June 2--9, 2022 at Divnomorskoe (near the town of Gelendzhik) at the Raduga sports and fitness center of the Don State Technical University. The conference was chaired by A. N. Shiryaev. Participants included leading scientists from Russia, France, Portugal, and Tadjikistan.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135658639","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
Turnpikes in Finite Markov Decision Processes and Random Walk 有限马尔可夫决策过程和随机漫步中的收费公路
4区 数学
Theory of Probability and its Applications Pub Date : 2023-05-01 DOI: 10.1137/s0040585x97t991325
A. B. Piunovskiy
{"title":"Turnpikes in Finite Markov Decision Processes and Random Walk","authors":"A. B. Piunovskiy","doi":"10.1137/s0040585x97t991325","DOIUrl":"https://doi.org/10.1137/s0040585x97t991325","url":null,"abstract":"In this paper we revise the theory of turnpikes in discounted Markov decision processes, prove the turnpike theorem for the undiscounted model, and apply the results to the specific random walk.KeywordsturnpikeMarkov decision processdiscounted rewardaverage rewardrandom walkstochastic knapsack problem","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136273938","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
Asymptotic Relative Efficiency of the Kendall and Spearman Correlation Statistics Kendall和Spearman相关统计量的渐近相对效率
4区 数学
Theory of Probability and its Applications Pub Date : 2023-05-01 DOI: 10.1137/s0040585x97t991313
I. Pinelis
{"title":"Asymptotic Relative Efficiency of the Kendall and Spearman Correlation Statistics","authors":"I. Pinelis","doi":"10.1137/s0040585x97t991313","DOIUrl":"https://doi.org/10.1137/s0040585x97t991313","url":null,"abstract":"A necessary and sufficient condition for Pitman's asymptotic relative efficiency of the Kendall and Spearman correlation statistics for the independence test to be $1$ is given, in terms of certain smoothness and nondegeneracy properties of the model. Corresponding easy-to-use and broadly applicable sufficient conditions are obtained. These conditions hold for most well-known models of dependence.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136273939","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 Asymptotic Expansion for Mathematical Expectation of a Renewal--Reward Process with Dependent Components and Heavy-Tailed Interarrival Times 具有依赖分量和重尾间隔时间的更新-奖励过程数学期望的渐近展开式
4区 数学
Theory of Probability and its Applications Pub Date : 2023-02-01 DOI: 10.1137/s0040585x97t991209
R. Aliyev, V. Bayramov
{"title":"On Asymptotic Expansion for Mathematical Expectation of a Renewal--Reward Process with Dependent Components and Heavy-Tailed Interarrival Times","authors":"R. Aliyev, V. Bayramov","doi":"10.1137/s0040585x97t991209","DOIUrl":"https://doi.org/10.1137/s0040585x97t991209","url":null,"abstract":"A renewal--reward process with dependent components and heavy-tailed interarrival times is investigated, and an asymptotic expansion as $ttoinfty$ for the expectation is derived.MSC codesrenewal processrenewal functionrenewal--reward processheavy-tailed distributionsubexponential distribution","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136178386","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
Generalized Poisson--Dirichlet Distributions Based on the Dickman Subordinator 基于Dickman从属子的广义Poisson—Dirichlet分布
4区 数学
Theory of Probability and its Applications Pub Date : 2023-02-01 DOI: 10.1137/s0040585x97t991167
R. Maller, S. Shemehsavar
{"title":"Generalized Poisson--Dirichlet Distributions Based on the Dickman Subordinator","authors":"R. Maller, S. Shemehsavar","doi":"10.1137/s0040585x97t991167","DOIUrl":"https://doi.org/10.1137/s0040585x97t991167","url":null,"abstract":"We study exchangeable random partitions based on an underlying Dickman subordinator and the corresponding family of Poisson--Dirichlet distributions. The large sample distribution of the vector representing the block sizes and the number of blocks in a partition of ${1,2,dots,n}$ is shown to be, after norming and centering, a product of independent Poissons and a normal distribution. In a species or gene sampling situation, these quantities represent the abundances and the numbers of species or genes observed in a sample of size $n$ from the corresponding Poisson--Dirichlet distribution. We include a summary of known convergence results concerning the Dickman subordinator in this context.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136178387","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
Uniqueness of the Inverse First-Passage Time Problem and the Shape of the Shiryaev Boundary 逆首次通过时间问题的唯一性和Shiryaev边界的形状
4区 数学
Theory of Probability and its Applications Pub Date : 2023-02-01 DOI: 10.1137/s0040585x97t991155
A. Klump, M. Kolb
{"title":"Uniqueness of the Inverse First-Passage Time Problem and the Shape of the Shiryaev Boundary","authors":"A. Klump, M. Kolb","doi":"10.1137/s0040585x97t991155","DOIUrl":"https://doi.org/10.1137/s0040585x97t991155","url":null,"abstract":"Given a distribution on the positive extended real line, the two-sided inverse first-passage time problem for Brownian motion asks for a function such that the first passage time of this function by a reflected Brownian motion has the given distribution. We combine the ideas of Ekström and Janson, which were developed within the scope of the one-sided inverse first-passage time problem, with the methods of De Masi et al., which were used in the context of free boundary problems, in order to give a different proof for the uniqueness for the two-sided inverse first-passage time problem by using a stochastic order relation. We provide criteria for qualitative properties of solutions of the inverse first-passage problem, which apply to the boundary corresponding to the exponential distribution.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135962649","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
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