Explicit bounds for the return probability of simple random walks

被引：1

作者：

Ball, K ^{[1
]}

Sterbenz, J

机构：

[1] Univ Minnesota, Inst Math & Its Applicat, Minneapolis, MN 55455 USA

[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2005年 / 18卷 / 02期

基金：

美国国家科学基金会;

关键词：

simple random walk; random walks; return probability; asymptotic probability;

D O I：

10.1007/s10959-003-2606-7

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 an exact computation of the second order term in the asymptotic expansion of the return probability, F-2n(d)(0,0), of a simple random walk on the d-dimensional cubic lattice. We also give an explicit bound on the remainder. In particular, we show that P-2n(d)(0, 0) < 2(d/4 pi n)(d/2) where n >= M = M(d) is explicitly given.

引用

页码：317 / 326

页数：10

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