Scaling limit of the local time of random walks conditioned to stay positive

被引：0

作者：

Hong, Wenming ^{[1
,2
]}

Sun, Mingyang ^{[1
,2
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Beijing Normal Univ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

来源：

JOURNAL OF APPLIED PROBABILITY | 2024年 / 61卷 / 03期

关键词：

Random walk; Bessel process; local time; conditioning to stay positive; CONVERGENCE; MEANDER; THEOREM;

D O I：

10.1017/jpr.2023.102

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove that the local time of random walks conditioned to stay positive converges to the corresponding local time of three-dimensional Bessel processes by proper scaling. Our proof is based on Tanaka's pathwise construction for conditioned random walks and the derivation of asymptotics for mixed moments of the local time.

引用

页码：1060 / 1074

页数：15

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