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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 Q3 STATISTICS & PROBABILITY
Journal of Theoretical Probability
Pub Date : 2023-09-25 DOI: 10.1007/s10959-023-01277-2
Andrzej Komisarski, Jacques Labuschagne
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
利用最近关于完全可混合概率分布的混合中心非唯一性的结果，我们得到如下结果:对于每个$$din {mathbb {N}}$$ d∈N和每个非空有界Borel集$$Bsubset {mathbb {R}}^d$$ B∧R d，存在一个d维概率分布$$varvec{mu }$$ μ满足以下条件:对于每个$$nge 3$$ n≥3和B上的每个概率分布$$varvec{nu }$$ ν，存在d维随机向量$${textbf{X}}_{varvec{nu },1},{textbf{X}}_{varvec{nu },2},dots ,{textbf{X}}_{varvec{nu },n}$$ X ν， 1, X ν， 2，⋯，X ν， n，使得$$frac{1}{n}({textbf{X}}_{varvec{nu },1}+{textbf{X}}_{varvec{nu },2}+dots +{textbf{X}}_{varvec{nu },n})sim varvec{nu }$$ 1 n (X ν， 1 + X ν， 2 +⋯+ X ν， n) ～ ν和$${textbf{X}}_{varvec{nu },i}sim varvec{mu }$$ X ν， i ～ μ对于$$i=1,2,dots ,n$$ i = 1,2，⋯n。我们还证明了关于集合B的有界性的假设不能完全省略，但它可以被大大削弱。
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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 Q3 STATISTICS & PROBABILITY
Journal of Theoretical Probability
Pub Date : 2023-09-25 DOI: 10.1007/s10959-023-01289-y
Shuyang Bai, He Tang
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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 Q3 STATISTICS & PROBABILITY
Journal of Theoretical Probability
Pub Date : 2023-09-22 DOI: 10.1007/s10959-023-01290-5
Xiaoyue Li, Xuerong Mao, Guoting Song
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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 Q3 STATISTICS & PROBABILITY
Journal of Theoretical Probability
Pub Date : 2023-08-25 DOI: 10.1007/s10959-023-01284-3
Chunsheng Ma
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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 Q3 STATISTICS & PROBABILITY
Journal of Theoretical Probability
Pub Date : 2023-08-14 DOI: 10.1007/s10959-023-01280-7
Liuyan Li, Junping Li
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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 Q3 STATISTICS & PROBABILITY
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 Q3 STATISTICS & PROBABILITY
Journal of Theoretical Probability
Pub Date : 2023-08-02 DOI: 10.1007/s10959-023-01279-0
Bingjun Wang, Hongjun Gao, Mingxia Yuan, Qingkun Xiao
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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 Q3 STATISTICS & PROBABILITY
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
Analysis of the Limiting Spectral Distribution of Large-dimensional General Information-Plus-Noise-Type Matrices 大维一般信息加噪声型矩阵的极限谱分布分析
4区 数学 Q3 STATISTICS & PROBABILITY
Journal of Theoretical Probability
Pub Date : 2023-07-28 DOI: 10.1007/s10959-023-01276-3
Huanchao Zhou, Jiang Hu, Zhidong Bai, Jack W. Silverstein
In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the “general information-plus-noise" type, as studied in Zhou (JTP 36:1203–1226, 2023). Through the equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and we show the determination criterion for its support. We also extend the result in Zhou (JTP 36:1203-1226, 2023) to allow for all possible ratios of row to column of the underlying random matrix.
本文推导了Zhou (JTP 36:1203 - 1226,2023)研究的“一般信息加噪声”型非中心协方差矩阵的极限谱分布的解析行为。通过定义其Stieltjes变换的方程，证明了极限分布有一个远离零的连续导数，导数为正的地方是解析的，并给出了其支持度的判定准则。我们还扩展了Zhou (JTP 36:20 3- 1226,2023)的结果，以允许底层随机矩阵的行与列的所有可能的比率。
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引用次数: 0
Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Discontinuous and Linear Growth Coefficients 具有不连续线性增长系数的Lévy过程驱动的广义倒向二重随机微分方程
IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Journal of Theoretical Probability
Pub Date : 2023-06-30 DOI: 10.1007/s10959-023-01270-9
J. Owo, A. Aman
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引用次数: 0
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