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


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


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.

Suggested Citation

  • den Hollander, F. & dos Santos, R. & Sidoravicius, V., 2013. "Law of large numbers for non-elliptic random walks in dynamic random environments," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 156-190.
  • Handle: RePEc:eee:spapps:v:123:y:2013:i:1:p:156-190 DOI: 10.1016/

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    References listed on IDEAS

    1. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    2. Paulauskas, Vygantas, 2010. "On Beveridge-Nelson decomposition and limit theorems for linear random fields," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 621-639, March.
    3. El Machkouri, Mohamed, 2002. "Kahane-Khintchine inequalities and functional central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 285-299, December.
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