Random walks in cones revisited

被引：2
作者：
Denisov, Denis [1 ]
Wachtel, Vitali [2 ]
机构：
[1] Univ Manchester, Dept Math, Manchester, England
[2] Bielefeld Univ, Fac Math, Bielefeld, Germany
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2024年 / 60卷 / 01期
关键词：
Random walk; Exit time; Harmonic function; Conditioned process; EXIT TIMES; POTENTIAL-THEORY; LIMIT-THEOREMS; BROWNIAN-MOTION; GREEN-FUNCTION; INEQUALITIES; BOUNDARY;
D O I：
10.1214/22-AIHP1331
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：
In this paper we continue our study of a multidimensional random walk with zero mean and finite variance killed on leaving a cone. We suggest a new approach that allows one to construct a positive harmonic function in Lipschitz cones under minimal moment conditions. This approach allows also to obtain more accurate information about the behaviour of the harmonic function not far from the boundary of the cone. We also prove limit theorems under new moment conditions.
引用
收藏
页码：126 / 166
页数：41
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