Almost sure relative stability of the overshoot of power law boundaries

被引：1
|
作者：
Doney, R. A.
Maller, R. A. [1 ]
机构：
[1] Australian Natl Univ, Sch Finance & Appl Stat, Canberra, ACT, Australia
[2] Univ Manchester, Dept Math, Manchester M60 1QD, Lancs, England
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2007年 / 20卷 / 01期
基金：
澳大利亚研究理事会;
关键词：
random walk; curved boundaries; overshoot of power-law boundaries;
D O I：
10.1007/s10959-006-0040-3
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 give necessary and sufficient conditions for the almost sure relative stability of the overshoot of a random walk when it exits from a two-sided symmetric region with curved boundaries. The boundaries are of power-law type, +/- rn(b), r > 0, n= 1, 2,..., where 0 <= b< 1, b not equal 1/ 2. In these cases, the a.s. stability occurs if and only if the mean step length of the random walk is finite and non-zero, or the step length has a finite variance and mean zero.
引用
收藏
页码：47 / 63
页数：17
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