发布求助
文献互助 智能选刊 最新文献

Journal of Theoretical Probability最新文献

筛选
英文 中文
Exact Modulus of Continuities for $$Lambda $$ -Fleming–Viot Processes with Brownian Spatial Motion 具有布朗空间运动的 $$Lambda $$ -Fleming-Viot 过程的精确连续性模量
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-04-03 DOI: 10.1007/s10959-024-01326-4
Huili Liu, Xiaowen Zhou
{"title":"Exact Modulus of Continuities for $$Lambda $$ -Fleming–Viot Processes with Brownian Spatial Motion","authors":"Huili Liu, Xiaowen Zhou","doi":"10.1007/s10959-024-01326-4","DOIUrl":"https://doi.org/10.1007/s10959-024-01326-4","url":null,"abstract":"<p>For a class of <span>(Lambda )</span>-Fleming–Viot processes with Brownian spatial motion in <span>(mathbb {R}^d)</span> whose associated <span>(Lambda )</span>-coalescents come down from infinity, we obtain sharp global and local moduli of continuity for the ancestral processes recovered from the associated lookdown representations. As applications, we establish both global and local moduli of continuity for the <span>(Lambda )</span>-Fleming–Viot support processes. In particular, if the <span>(Lambda )</span>-coalescent is the Beta<span>((2-beta ,beta ))</span> coalescent for <span>(beta in (1,2])</span> with <span>(beta =2)</span> corresponding to Kingman’s coalescent, then for <span>(h(t)=sqrt{tlog (1/t)})</span>, the global modulus of continuity holds for the support process with modulus function <span>(sqrt{2beta /(beta -1)}h(t))</span>, and both the left and right local moduli of continuity hold for the support process with modulus function <span>(sqrt{2/(beta -1)}h(t))</span>.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561947","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
Approximation Schemes for McKean–Vlasov and Boltzmann-Type Equations (Error Analysis in Total Variation Distance) 麦金-弗拉索夫方程和波尔兹曼方程的近似方案（总变异距离误差分析）
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-04-03 DOI: 10.1007/s10959-024-01324-6
Yifeng Qin
{"title":"Approximation Schemes for McKean–Vlasov and Boltzmann-Type Equations (Error Analysis in Total Variation Distance)","authors":"Yifeng Qin","doi":"10.1007/s10959-024-01324-6","DOIUrl":"https://doi.org/10.1007/s10959-024-01324-6","url":null,"abstract":"<p>We deal with McKean–Vlasov and Boltzmann-type jump equations. This means that the coefficients of the stochastic equation depend on the law of the solution, and the equation is driven by a Poisson point measure with intensity measure which depends on the law of the solution as well. Alfonsi and Bally (Construction of Boltzmann and McKean Vlasov type flows (the sewing lemma approach), 2021, arXiv:2105.12677) have proved that under some suitable conditions, the solution <span>(X_t)</span> of such equation exists and is unique. One also proves that <span>(X_t)</span> is the probabilistic interpretation of an analytical weak equation. Moreover, the Euler scheme <span>(X_t^{{mathcal {P}}})</span> of this equation converges to <span>(X_t)</span> in Wasserstein distance. In this paper, under more restrictive assumptions, we show that the Euler scheme <span>(X_t^{{mathcal {P}}})</span> converges to <span>(X_t)</span> in total variation distance and <span>(X_t)</span> has a smooth density (which is a function solution of the analytical weak equation). On the other hand, in view of simulation, we use a truncated Euler scheme <span>(X^{{mathcal {P}},M}_t)</span> which has a finite numbers of jumps in any compact interval. We prove that <span>(X^{{mathcal {P}},M}_{t})</span> also converges to <span>(X_t)</span> in total variation distance. Finally, we give an algorithm based on a particle system associated with <span>(X^{{mathcal {P}},M}_t)</span> in order to approximate the density of the law of <span>(X_t)</span>. Complete estimates of the error are obtained.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561739","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
Limit Behavior in High-Dimensional Regime for the Wishart Tensors in Wiener Chaos 维纳混沌中 Wishart 张量的高维极限行为
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-03-30 DOI: 10.1007/s10959-024-01328-2
Rémy Dhoyer, C. Tudor
{"title":"Limit Behavior in High-Dimensional Regime for the Wishart Tensors in Wiener Chaos","authors":"Rémy Dhoyer, C. Tudor","doi":"10.1007/s10959-024-01328-2","DOIUrl":"https://doi.org/10.1007/s10959-024-01328-2","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140362929","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 Behaviors for Random Geometric Series 随机几何数列的渐近行为
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-03-29 DOI: 10.1007/s10959-024-01327-3
Fuqing Gao, Yunshi Gao, Xianjie Xia
{"title":"Asymptotic Behaviors for Random Geometric Series","authors":"Fuqing Gao, Yunshi Gao, Xianjie Xia","doi":"10.1007/s10959-024-01327-3","DOIUrl":"https://doi.org/10.1007/s10959-024-01327-3","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140366629","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
A Note on the Markovian SIR Epidemic on a Random Graph with Given Degrees 关于给定度数随机图上马尔可夫 SIR 流行病的说明
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-03-24 DOI: 10.1007/s10959-024-01320-w
{"title":"A Note on the Markovian SIR Epidemic on a Random Graph with Given Degrees","authors":"","doi":"10.1007/s10959-024-01320-w","DOIUrl":"https://doi.org/10.1007/s10959-024-01320-w","url":null,"abstract":"<h3>Abstract</h3> <p>We consider a Markovian model of an SIR epidemic spreading on a contact graph that is drawn uniformly at random from the set of all graphs with <em>n</em> vertices and given vertex degrees. Janson, Luczak and Windridge (Random Struct Alg 45(4):724–761, 2014) prove that the evolution of such an epidemic is well approximated by the solution to a simple set of differential equations, thus providing probabilistic underpinnings to the works of Miller (J Math Biol 62(3):349–358, 2011) and Volz (J Math Biol 56(3):293–310, 2008). The present paper provides an additional probabilistic interpretation of the limiting deterministic functions in Janson, Luczak and Windridge (Random Struct Alg 45(4):724–761, 2014), thus clarifying further the connection between their results and the results of Miller and Volz.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140202537","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
Exit Times for a Discrete Markov Additive Process 离散马尔可夫加法过程的退出时间
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-03-17 DOI: 10.1007/s10959-024-01322-8
Zbigniew Palmowski, Lewis Ramsden, Apostolos D. Papaioannou
{"title":"Exit Times for a Discrete Markov Additive Process","authors":"Zbigniew Palmowski, Lewis Ramsden, Apostolos D. Papaioannou","doi":"10.1007/s10959-024-01322-8","DOIUrl":"https://doi.org/10.1007/s10959-024-01322-8","url":null,"abstract":"<p>In this paper, we consider (upward skip-free) discrete-time and discrete-space Markov additive chains (MACs) and develop the theory for the so-called <span>(widetilde{{textbf {W}}})</span> and <span>(widetilde{{textbf {Z}}})</span> scale matrices, which are shown to play a vital role in the determination of a number of exit problems and related fluctuation identities. The theory developed in this fully discrete set-up follows similar lines of reasoning as the analogous theory for Markov additive processes in continuous time and is exploited to obtain the probabilistic construction of the scale matrices, identify the form of the generating function and produce a simple recursion relation for <span>(widetilde{{textbf {W}}})</span>, as well as its connection with the so-called occupation mass formula. In addition to the standard one- and two-sided exit problems (upwards and downwards), we also derive distributional characteristics for a number of quantities related to the one- and two-sided ‘reflected’ processes.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154182","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
Hausdorff Measure and Uniform Dimension for Space-Time Anisotropic Gaussian Random Fields 时空各向异性高斯随机场的豪斯多夫量和均匀维度
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-03-15 DOI: 10.1007/s10959-024-01323-7
Weijie Yuan, Zhenlong Chen
{"title":"Hausdorff Measure and Uniform Dimension for Space-Time Anisotropic Gaussian Random Fields","authors":"Weijie Yuan, Zhenlong Chen","doi":"10.1007/s10959-024-01323-7","DOIUrl":"https://doi.org/10.1007/s10959-024-01323-7","url":null,"abstract":"<p>Let <span>(X={ X(t), tin mathbb {R}^{N}} )</span> be a centered space-time anisotropic Gaussian random field in <span>(mathbb {R}^d)</span> with stationary increments, where the components <span>(X_{i}(i=1,ldots ,d))</span> are independent but distributed differently. Under certain conditions, we not only give the Hausdorff dimension of the graph sets of <i>X</i> in the asymmetric metric in the recurrent case, but also determine the exact Hausdorff measure functions of the graph sets of <i>X</i> in the transient and recurrent cases, respectively. Moreover, we establish a uniform Hausdorff dimension result for the image sets of <i>X</i>. Our results extend the corresponding results on fractional Brownian motion and space or time anisotropic Gaussian random fields.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154092","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
The Voter Model with a Slow Membrane 带慢膜的选民模型
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-03-13 DOI: 10.1007/s10959-024-01321-9
Linjie Zhao, Xiaofeng Xue
{"title":"The Voter Model with a Slow Membrane","authors":"Linjie Zhao, Xiaofeng Xue","doi":"10.1007/s10959-024-01321-9","DOIUrl":"https://doi.org/10.1007/s10959-024-01321-9","url":null,"abstract":"<p>We introduce the voter model on the infinite integer lattice with a slow membrane and investigate its hydrodynamic behavior and nonequilibrium fluctuations. The voter model is one of the classical interacting particle systems with state space <span>({0,1}^{mathbb Z^d})</span>. In our model, a voter adopts one of its neighbors’ opinion at rate one except for neighbors crossing the hyperplane <span>({x:x_1 = 1/2})</span>, where the rate is <span>(alpha N^{-beta })</span> and thus is called a slow membrane. Above, <span>(alpha &gt;0 textrm{and} beta ge 0)</span> are given parameters and the positive integer <i>N</i> is a scaling parameter. We consider the limit <span>(N rightarrow infty )</span> and prove that the hydrodynamic limits are given by the heat equation without or with Robin/Neumann conditions depending on the values of <span>(beta )</span>. We also consider the nonequilibrium fluctuations, where the limit is described by generalized Ornstein–Uhlenbeck processes with certain boundary conditions corresponding to the hydrodynamic equation.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116330","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
Rough Differential Equations Containing Path-Dependent Bounded Variation Terms 包含路径依赖性有界变量项的粗糙微分方程
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-03-08 DOI: 10.1007/s10959-024-01319-3
Shigeki Aida
{"title":"Rough Differential Equations Containing Path-Dependent Bounded Variation Terms","authors":"Shigeki Aida","doi":"10.1007/s10959-024-01319-3","DOIUrl":"https://doi.org/10.1007/s10959-024-01319-3","url":null,"abstract":"<p>We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori estimate of solutions. These equations include classical path-dependent stochastic differential equations containing running maximum processes and normal reflection terms. We apply these results to determine the topological support of the solution processes.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075488","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
Homogenization of a Multivariate Diffusion with Semipermeable Interfaces 带半透界面的多元扩散的均质化
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-03-07 DOI: 10.1007/s10959-024-01317-5
{"title":"Homogenization of a Multivariate Diffusion with Semipermeable Interfaces","authors":"","doi":"10.1007/s10959-024-01317-5","DOIUrl":"https://doi.org/10.1007/s10959-024-01317-5","url":null,"abstract":"<h3>Abstract</h3> <p>We study the homogenization problem for a system of stochastic differential equations with local time terms that models a multivariate diffusion in the presence of semipermeable hyperplane interfaces with oblique penetration. We show that this system has a unique weak solution and determine its weak limit as the distances between the interfaces converge to zero. In the limit, the singular local times terms vanish and give rise to an additional regular <em>interface-induced</em> drift.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075635","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信