Positively and negatively excited random walks on integers, with branching processes

被引：38

作者：

Kosygina, Elena ^{[1
]}

Zerner, Martin P. W. ^{[2
]}

机构：

[1] CUNY Bernard M Baruch Coll, Dept Math, New York, NY 10010 USA

[2] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2008年 / 13卷

关键词：

Central limit theorem; excited random walk; law of large numbers; positive and negative cookies; recurrence; renewal structure; transience;

D O I：

10.1214/EJP.v13-572

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 excited random walks on Z with a bounded number of i.i.d. cookies per site which may induce drifts both to the left and to the right. We extend the criteria for recurrence and transience by M. Zerner and for positivity of speed by A.-L. Basdevant and A. Singh to this case and also prove an annealed central limit theorem. The proofs are based on results from the literature concerning branching processes with migration and make use of a certain renewal structure.

引用

页码：1952 / 1979

页数：28

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