FIRST-PASSAGE TIMES FOR RANDOM WALKS WITH NONIDENTICALLY DISTRIBUTED INCREMENTS

被引：16

作者：

Denisov, Denis ^{[1
]}

Sakhanenko, Alexander ^{[2
]}

Wachtel, Vitali ^{[3
]}

机构：

[1] Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Univ Augsburg, Inst Math, D-86135 Augsburg, Germany

来源：

ANNALS OF PROBABILITY | 2018年 / 46卷 / 06期

关键词：

Random walk; Brownian motion; first-passage time; overshoot; moving boundary; LIMIT-THEOREMS; RANDOM-VARIABLES; MOVING BOUNDARY; CONVERGENCE; STAY; EXIT;

D O I：

10.1214/17-AOP1248

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 consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first passage times over moving boundaries. Furthermore, we prove that a properly rescaled random walk conditioned to stay above the boundary up to time n converges, as n -> infinity towards the Brownian meander.

引用

页码：3313 / 3350

页数：38

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