Journal of Theoretical Probability最新文献

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Cutpoints of (1,2) and (2,1) Random Walks on the Lattice of Positive Half Line (1,2)和(2,1)随机漫步在正半直线格上的截点

4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability

Pub Date : 2023-10-13 DOI: 10.1007/s10959-023-01293-2

Lanlan Tang, Hua-Ming Wang

引用次数: 0

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 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability

Pub Date : 2023-09-29 DOI: 10.1007/s10959-023-01283-4

Denis Denisov, Vitali Wachtel

Abstract We consider an asymptotically stable multidimensional random walk $$S(n)=(S_1(n),ldots , S_d(n) )$$ S ( n ) = ( S 1 ( n ) , … , S d ( n ) ) . For every vector $$x=(x_1ldots ,x_d)$$ x = ( x 1 … , x d ) with $$x_1ge 0$$ x 1 ≥ 0 , let $$tau _x:=min {n>0: x_{1}+S_1(n)le 0}$$ τ x : = min { n > 0 : x 1 + S 1 ( n ) ≤ 0 } be the first time the random walk $$x+S(n)$$ x + S ( n ) leaves the upper half space. We obtain the asymptotics of $$p_n(x,y):= {textbf{P}}(x+S(n) in y+Delta , tau _x>n)$$ p n ( x , y ) : = P ( x + S ( n ) ∈ y + Δ , τ x > n )

我们认为不合理的是，我们认为是一种复杂的多多维的稳定步行S(n)=(S_1(n)，ldots, S_d(n) $S(n)为每一个向量$ x = (x_1 ldots, x_d) $ ... 1 x = (x, x, d)和$ x_1 ge 0 $ x 1≥0,则让$知道_x: = min { {n> 0: x_ {1} + S_1 (n)的le 0 $τx: = min {n >0:×1 + S (n)≤0}成为《随机漫步第一次$ x + S (n) $ x + S (n)的树叶上半空间。asymptotics》我们得到$ p_n (x, y): = P { textbf {}} (x + S + y (n) 中三角洲,知道_x> n) $ $ P (x, y): = P (x + y + S (n)∈xΔ,τ>n)美国n tends to无限,在$ $Δ三角洲是一个固定立方体。从这一点,我们得到《绿功能(local asymptotics for $ G (x, y): sum = _n p_n (x, y) $ G (x, y): =∑n p n (x, y),美国$ | | $ | | y和y - x或x $ | | $ | | tend to无限。

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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 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability

Pub Date : 2023-09-25 DOI: 10.1007/s10959-023-01288-z

Ying Hu, Remi Moreau, Falei Wang

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 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。

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

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

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

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

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

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

引用次数: 0

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