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Green Function for an Asymptotically Stable Random Walk in a Half Space 半空间中渐近稳定随机漫步的格林函数
4区 数学
Journal of Theoretical Probability Pub Date : 2023-09-29 DOI: 10.1007/s10959-023-01283-4
Denis Denisov, Vitali Wachtel
{"title":"Green Function for an Asymptotically Stable Random Walk in a Half Space","authors":"Denis Denisov, Vitali Wachtel","doi":"10.1007/s10959-023-01283-4","DOIUrl":"https://doi.org/10.1007/s10959-023-01283-4","url":null,"abstract":"Abstract We consider an asymptotically stable multidimensional random walk $$S(n)=(S_1(n),ldots , S_d(n) )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . For every vector $$x=(x_1ldots ,x_d)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>=</mml:mo> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> with $$x_1ge 0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , let $$tau _x:=min {n>0: x_{1}+S_1(n)le 0}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>τ</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:mo>:</mml:mo> <mml:mo>=</mml:mo> <mml:mo>min</mml:mo> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>n</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mn>0</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:mrow> </mml:math> be the first time the random walk $$x+S(n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>+</mml:mo> <mml:mi>S</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> leaves the upper half space. We obtain the asymptotics of $$p_n(x,y):= {textbf{P}}(x+S(n) in y+Delta , tau _x>n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>:</mml:mo> <mml:mo>=</mml:mo> <mml:mi>P</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>+</mml:mo> <mml:mi>S</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∈</mml:mo> <mml:mi>y</mml:mi> <mml:mo>+</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>τ</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:mo>></mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135246621","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
General Mean Reflected Backward Stochastic Differential Equations 一般均值反映后向随机微分方程
4区 数学
Journal of Theoretical Probability Pub Date : 2023-09-25 DOI: 10.1007/s10959-023-01288-z
Ying Hu, Remi Moreau, Falei Wang
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引用次数: 0
The Distributions of the Mean of Random Vectors with Fixed Marginal Distribution 具有固定边际分布的随机向量的均值分布
4区 数学
Journal of Theoretical Probability Pub Date : 2023-09-25 DOI: 10.1007/s10959-023-01277-2
Andrzej Komisarski, Jacques Labuschagne
{"title":"The Distributions of the Mean of Random Vectors with Fixed Marginal Distribution","authors":"Andrzej Komisarski, Jacques Labuschagne","doi":"10.1007/s10959-023-01277-2","DOIUrl":"https://doi.org/10.1007/s10959-023-01277-2","url":null,"abstract":"Abstract Using recent results concerning non-uniqueness of the center of the mix for completely mixable probability distributions, we obtain the following result: For each $$din {mathbb {N}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> and each non-empty bounded Borel set $$Bsubset {mathbb {R}}^d$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> </mml:mrow> </mml:math> , there exists a d -dimensional probability distribution $$varvec{mu }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> </mml:math> satisfying the following: For each $$nge 3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> and each probability distribution $$varvec{nu }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> </mml:math> on B , there exist d -dimensional random vectors $${textbf{X}}_{varvec{nu },1},{textbf{X}}_{varvec{nu },2},dots ,{textbf{X}}_{varvec{nu },n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> such that $$frac{1}{n}({textbf{X}}_{varvec{nu },1}+{textbf{X}}_{varvec{nu },2}+dots +{textbf{X}}_{varvec{nu },n})sim varvec{nu }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mi>n</mml:mi> </mml:mfrac> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∼</mml:mo> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> </mml:mrow> </mml:math> and $${textbf{X}}_{varvec{nu },i}sim varvec{mu }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mro","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135815919","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
Joint Sum-and-Max Limit for a Class of Long-Range Dependent Processes with Heavy Tails 一类具有重尾的长程相关过程的联合和极大极限
4区 数学
Journal of Theoretical Probability Pub Date : 2023-09-25 DOI: 10.1007/s10959-023-01289-y
Shuyang Bai, He Tang
{"title":"Joint Sum-and-Max Limit for a Class of Long-Range Dependent Processes with Heavy Tails","authors":"Shuyang Bai, He Tang","doi":"10.1007/s10959-023-01289-y","DOIUrl":"https://doi.org/10.1007/s10959-023-01289-y","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135816101","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
Explicit Approximation of Invariant Measure for Stochastic Delay Differential Equations with the Nonlinear Diffusion Term 具有非线性扩散项的随机时滞微分方程不变测度的显式逼近
4区 数学
Journal of Theoretical Probability Pub Date : 2023-09-22 DOI: 10.1007/s10959-023-01290-5
Xiaoyue Li, Xuerong Mao, Guoting Song
{"title":"Explicit Approximation of Invariant Measure for Stochastic Delay Differential Equations with the Nonlinear Diffusion Term","authors":"Xiaoyue Li, Xuerong Mao, Guoting Song","doi":"10.1007/s10959-023-01290-5","DOIUrl":"https://doi.org/10.1007/s10959-023-01290-5","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136016686","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
Bifractional Brownian Motions on Metric Spaces 度量空间上的双分数布朗运动
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-08-25 DOI: 10.1007/s10959-023-01284-3
Chunsheng Ma
{"title":"Bifractional Brownian Motions on Metric Spaces","authors":"Chunsheng Ma","doi":"10.1007/s10959-023-01284-3","DOIUrl":"https://doi.org/10.1007/s10959-023-01284-3","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47461005","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
Harmonic Moments and Large Deviations for the Markov Branching Process with Immigration 具有迁移的马尔可夫分支过程的调和矩和大偏差
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-08-14 DOI: 10.1007/s10959-023-01280-7
Liuyan Li, Junping Li
{"title":"Harmonic Moments and Large Deviations for the Markov Branching Process with Immigration","authors":"Liuyan Li, Junping Li","doi":"10.1007/s10959-023-01280-7","DOIUrl":"https://doi.org/10.1007/s10959-023-01280-7","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43087086","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
Sub-exponentiality in Statistical Exponential Models 统计指数模型中的次指数性
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-08-12 DOI: 10.1007/s10959-023-01281-6
B. Trivellato
{"title":"Sub-exponentiality in Statistical Exponential Models","authors":"B. Trivellato","doi":"10.1007/s10959-023-01281-6","DOIUrl":"https://doi.org/10.1007/s10959-023-01281-6","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48036667","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
Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion Under Monotonicity Condition 单调条件下G-布朗运动驱动的反射倒向随机微分方程
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-08-02 DOI: 10.1007/s10959-023-01279-0
Bingjun Wang, Hongjun Gao, Mingxia Yuan, Qingkun Xiao
{"title":"Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion Under Monotonicity Condition","authors":"Bingjun Wang, Hongjun Gao, Mingxia Yuan, Qingkun Xiao","doi":"10.1007/s10959-023-01279-0","DOIUrl":"https://doi.org/10.1007/s10959-023-01279-0","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41761584","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 Strong Convergence Rate of the Averaging Principle for Two-Time-Scale Forward-Backward Stochastic Differential Equations 双时间尺度正反向随机微分方程平均原理的强收敛速率
IF 0.8 4区 数学
Journal of Theoretical Probability Pub Date : 2023-07-29 DOI: 10.1007/s10959-023-01278-1
Jie Xu, Qiqi Lian
{"title":"A Strong Convergence Rate of the Averaging Principle for Two-Time-Scale Forward-Backward Stochastic Differential Equations","authors":"Jie Xu, Qiqi Lian","doi":"10.1007/s10959-023-01278-1","DOIUrl":"https://doi.org/10.1007/s10959-023-01278-1","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41910854","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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