Law of large numbers for non-elliptic random walks in dynamic random environments

F. den Hollander, R. dos Santos and V. Sidoravicius

Stochastic Processes and their Applications, 2013, vol. 123, issue 1, 156-190

Abstract: We prove a law of large numbers for a class of Zd-valued random walks in dynamic random environments, including non-elliptic examples. We assume for the random environment a mixing property called conditional cone-mixing and that the random walk tends to stay inside wide enough space–time cones. The proof is based on a generalization of a regeneration scheme developed by Comets and Zeitouni (2004) [5] for static random environments and adapted by Avena et al. (2011) [2] to dynamic random environments. A number of one-dimensional examples are given. In some cases, the sign of the speed can be determined.

Keywords: Random walk; Dynamic random environment; Non-elliptic; Conditional cone-mixing; Regeneration; Law of large numbers (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:1:p:156-190

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DOI: 10.1016/j.spa.2012.09.002

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