MARTIN CAPACITY FOR MARKOV-CHAINS

被引：25

作者：

BENJAMINI, I

PEMANTLE, R

PERES, Y

机构：

[1] UNIV WISCONSIN,DEPT MATH,MADISON,WI 53706

[2] UNIV CALIF BERKELEY,DEPT STAT,BERKELEY,CA 94720

来源：

ANNALS OF PROBABILITY | 1995年 / 23卷 / 03期

关键词：

CAPACITY; MARKOV CHAIN; HITTING PROBABILITY; BROWNIAN MOTION; TREE; PERCOLATION;

D O I：

10.1214/aop/1176988187

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：

The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Lambda is classically estimated using the capacity of Lambda with respect to the Green kernel G(x, y). We show that replacing the Green kernel by the Martin kernel G(x, y)/G(0, y) yields improved estimates, which are exact up to a factor of 2. These estimates are applied to random walks on lattices and also to explain a connection found by Lyons between capacity and percolation on trees.

引用

页码：1332 / 1346

页数：15

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