Recurrence of cocycles and stationary random walks

Abstract

We survey distributional properties of ${\mathbb{R}}^d$-valued cocycles of finite measure preserving ergodic transformations (or, equivalently, of stationary random walks in ${\mathbb{R}}^d$) which determine recurrence or transience.

Published at http://dx.doi.org/10.1214/074921706000000112 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)