Recurrence of cocycles and stationary random walks. (English) Zbl 1137.37004

Denteneer, Dee (ed.) et al., Dynamics and stochastics. Festschrift in honor of M. S. Keane. Selected papers based on the presentations at the conference ‘Dynamical systems, probability theory, and statistical mechanics’, Eindhoven, The Netherlands, January 3–7, 2005, on the occasion of the 65th birthday of Mike S. Keane. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 0-940600-64-1/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 48, 78-84 (2006).
A survey on recurrence properties of stationary random walks on \(\mathbb R^d\), formulated as \(\mathbb R^d\)-valued cocycles over ergodic transformations on a probability space, is given. Two new results, relating recurrence with distributional properties of the cocycle, are derived.
For the entire collection see [Zbl 1113.60008].


37A20 Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations
60G50 Sums of independent random variables; random walks
37A50 Dynamical systems and their relations with probability theory and stochastic processes
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