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Asymptotic Expansions for Additive Measures of Branching Brownian Motions 分支布朗运动加法量的渐近展开
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-06-19 DOI: 10.1007/s10959-024-01347-z
Haojie Hou, Yan-Xia Ren, Renming Song
{"title":"Asymptotic Expansions for Additive Measures of Branching Brownian Motions","authors":"Haojie Hou, Yan-Xia Ren, Renming Song","doi":"10.1007/s10959-024-01347-z","DOIUrl":"https://doi.org/10.1007/s10959-024-01347-z","url":null,"abstract":"<p>Let <i>N</i>(<i>t</i>) be the collection of particles alive at time <i>t</i> in a branching Brownian motion in <span>(mathbb {R}^d)</span>, and for <span>(uin N(t))</span>, let <span>({textbf{X}}_u(t))</span> be the position of particle <i>u</i> at time <i>t</i>. For <span>(theta in mathbb {R}^d)</span>, we define the additive measures of the branching Brownian motion by </p><span>$$begin{aligned}{} &amp; {} mu _t^theta (textrm{d}{textbf{x}}):= e^{-(1+frac{Vert theta Vert ^2}{2})t}sum _{uin N(t)} e^{-theta cdot {textbf{X}}_u(t)} delta _{left( {textbf{X}}_u(t)+theta tright) }(textrm{d}{textbf{x}}),{} &amp; {} quad textrm{here},, Vert theta Vert mathrm {is, the, Euclidean, norm, of},, theta . end{aligned}$$</span><p>In this paper, under some conditions on the offspring distribution, we give asymptotic expansions of arbitrary order for <span>(mu _t^theta (({textbf{a}}, {textbf{b}}]))</span> and <span>(mu _t^theta ((-infty , {textbf{a}}]))</span> for <span>(theta in mathbb {R}^d)</span> with <span>(Vert theta Vert &lt;sqrt{2})</span>, where <span>((textbf{a}, textbf{b}]:=(a_1, b_1]times cdots times (a_d, b_d])</span> and <span>((-infty , textbf{a}]:=(-infty , a_1]times cdots times (-infty , a_d])</span> for <span>(textbf{a}=(a_1,cdots , a_d))</span> and <span>(textbf{b}=(b_1,cdots , b_d))</span>. These expansions sharpen the asymptotic results of Asmussen and Kaplan (Stoch Process Appl 4(1):1–13, 1976) and Kang (J Korean Math Soc 36(1): 139–157, 1999) and are analogs of the expansions in Gao and Liu (Sci China Math 64(12):2759–2774, 2021) and Révész et al. (J Appl Probab 42(4):1081–1094, 2005) for branching Wiener processes (a particular class of branching random walks) corresponding to <span>(theta ={textbf{0}})</span>.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527796","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
Harnack Inequality for Distribution Dependent Second-Order Stochastic Differential Equations 分布相关二阶随机微分方程的哈纳克不等式
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-06-18 DOI: 10.1007/s10959-024-01346-0
Xing Huang, Xiaochen Ma
{"title":"Harnack Inequality for Distribution Dependent Second-Order Stochastic Differential Equations","authors":"Xing Huang, Xiaochen Ma","doi":"10.1007/s10959-024-01346-0","DOIUrl":"https://doi.org/10.1007/s10959-024-01346-0","url":null,"abstract":"<p>By investigating the regularity of the nonlinear semigroup <span>(P_t^*)</span> associated with the distribution dependent second-order stochastic differential equations, the Harnack inequality is derived when the drift is Lipschitz continuous in the measure variable under the distance induced by the functions being <span>(beta )</span>-Hölder continuous (with <span>(beta &gt; frac{2}{3})</span>) on the degenerate component and square root of Dini continuous on the non-degenerate one. The results extend the existing ones in which the drift is Lipschitz continuous in <span>(L^2)</span>-Wasserstein distance.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527717","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
Large Deviation Principle for Stochastic Reaction–Diffusion Equations with Superlinear Drift on $$mathbb {R}$$ Driven by Space–Time White Noise 时空白噪声驱动 $$mathbb {R}$ 上超线性漂移的随机反应-扩散方程的大偏差原理
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-06-17 DOI: 10.1007/s10959-024-01345-1
Yue Li, Shijie Shang, Jianliang Zhai
{"title":"Large Deviation Principle for Stochastic Reaction–Diffusion Equations with Superlinear Drift on $$mathbb {R}$$ Driven by Space–Time White Noise","authors":"Yue Li, Shijie Shang, Jianliang Zhai","doi":"10.1007/s10959-024-01345-1","DOIUrl":"https://doi.org/10.1007/s10959-024-01345-1","url":null,"abstract":"<p>In this paper, we consider stochastic reaction–diffusion equations with superlinear drift on the real line <span>(mathbb {R})</span> driven by space–time white noise. A Freidlin–Wentzell large deviation principle is established by a modified weak convergence method on the space <span>(C([0,T], C_textrm{tem}(mathbb {R})))</span>, where <span>(C_textrm{tem}(mathbb {R}):={fin C(mathbb {R}): sup _{xin mathbb {R}} left( |f(x)|e^{-lambda |x|}right) &lt;infty text { for any } lambda &gt;0})</span>. Obtaining the main result in this paper is challenging due to the setting of unbounded domain, the space–time white noise, and the superlinear drift term without dissipation. To overcome these difficulties, the specially designed family of norms on the Fréchet space <span>(C([0,T], C_textrm{tem}(mathbb {R})))</span>, one-order moment estimates of the stochastic convolution, and two nonlinear Gronwall-type inequalities play an important role.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529070","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
Another Look at Stein’s Method for Studentized Nonlinear Statistics with an Application to U-Statistics 斯坦因非线性统计研究方法在 U 统计中的另一种应用
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-06-15 DOI: 10.1007/s10959-024-01350-4
Dennis Leung, Qi-Man Shao, Liqian Zhang
{"title":"Another Look at Stein’s Method for Studentized Nonlinear Statistics with an Application to U-Statistics","authors":"Dennis Leung, Qi-Man Shao, Liqian Zhang","doi":"10.1007/s10959-024-01350-4","DOIUrl":"https://doi.org/10.1007/s10959-024-01350-4","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141336792","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 Transport Map Computed by Iterated Function System 用迭代函数系统计算的运输图
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-06-13 DOI: 10.1007/s10959-024-01349-x
Judy Yangjun Lin, Huoxia Liu
{"title":"The Transport Map Computed by Iterated Function System","authors":"Judy Yangjun Lin, Huoxia Liu","doi":"10.1007/s10959-024-01349-x","DOIUrl":"https://doi.org/10.1007/s10959-024-01349-x","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141349148","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
Hitting with Probability One for Stochastic Heat Equations with Additive Noise 带有加性噪声的随机热方程的概率一命中率
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-06-06 DOI: 10.1007/s10959-024-01342-4
Robert C. Dalang, Fei Pu
{"title":"Hitting with Probability One for Stochastic Heat Equations with Additive Noise","authors":"Robert C. Dalang, Fei Pu","doi":"10.1007/s10959-024-01342-4","DOIUrl":"https://doi.org/10.1007/s10959-024-01342-4","url":null,"abstract":"<p>We study the hitting probabilities of the solution to a system of <i>d</i> stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive <span>((d-6))</span>-dimensional capacity, the solution visits this set almost surely.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551865","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
Density Fluctuations for the Multi-Species Stirring Process 多物种搅拌过程的密度波动
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-05-28 DOI: 10.1007/s10959-024-01340-6
Francesco Casini, Cristian Giardinà, Frank Redig
{"title":"Density Fluctuations for the Multi-Species Stirring Process","authors":"Francesco Casini, Cristian Giardinà, Frank Redig","doi":"10.1007/s10959-024-01340-6","DOIUrl":"https://doi.org/10.1007/s10959-024-01340-6","url":null,"abstract":"<p>We study the density fluctuations at equilibrium of the multi-species stirring process, a natural multi-type generalization of the symmetric (partial) exclusion process. In the diffusive scaling limit, the resulting process is a system of infinite-dimensional Ornstein–Uhlenbeck processes that are coupled in the noise terms. This shows that at the level of equilibrium fluctuations the species start to interact, even though at the level of the hydrodynamic limit each species diffuses separately. We consider also a generalization to a multi-species stirring process with a linear reaction term arising from species mutation. The general techniques used in the proof are based on the Dynkin martingale approach, combined with duality for the computation of the covariances.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141166853","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
Limiting Spectral Radii for Products of Ginibre Matrices and Their Inverses 吉尼布雷矩阵及其倒数乘积的极限谱半径
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-05-24 DOI: 10.1007/s10959-024-01341-5
Xiansi Ma, Yongcheng Qi
{"title":"Limiting Spectral Radii for Products of Ginibre Matrices and Their Inverses","authors":"Xiansi Ma, Yongcheng Qi","doi":"10.1007/s10959-024-01341-5","DOIUrl":"https://doi.org/10.1007/s10959-024-01341-5","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141101228","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
Explosion Rates for Continuous-State Branching Processes in a Lévy Environment 列维环境下连续状态分支过程的爆炸率
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-05-24 DOI: 10.1007/s10959-024-01338-0
Natalia Cardona-Tobón, Juan Carlos Pardo
{"title":"Explosion Rates for Continuous-State Branching Processes in a Lévy Environment","authors":"Natalia Cardona-Tobón, Juan Carlos Pardo","doi":"10.1007/s10959-024-01338-0","DOIUrl":"https://doi.org/10.1007/s10959-024-01338-0","url":null,"abstract":"<p>Here, we study the long-term behaviour of the non-explosion probability for continuous-state branching processes in a Lévy environment when the branching mechanism is given by the negative of the Laplace exponent of a subordinator. In order to do so, we study the law of this family of processes in the infinite mean case and provide necessary and sufficient conditions for the process to be conservative, i.e. that the process does not explode in finite time a.s. In addition, we establish precise rates for the non-explosion probabilities in the subcritical and critical regimes, first found by Palau et al. (ALEA Lat Am J Probab Math Stat 13(2):1235–1258, 2016) in the case when the branching mechanism is given by the negative of the Laplace exponent of a stable subordinator.\u0000</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147115","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
An Analogue of the Klebanov Theorem for Locally Compact Abelian Groups 局部紧凑无性群的克勒巴诺夫定理类比
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2024-05-22 DOI: 10.1007/s10959-024-01339-z
M. Myronyuk
{"title":"An Analogue of the Klebanov Theorem for Locally Compact Abelian Groups","authors":"M. Myronyuk","doi":"10.1007/s10959-024-01339-z","DOIUrl":"https://doi.org/10.1007/s10959-024-01339-z","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141109407","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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