Acta mathematica scientia, Series B >
RENEWAL THEOREM FOR (L, 1)-RANDOM WALK IN RANDOM ENVIRONMENT
Received date: 2012-06-19
Revised date: 2012-11-06
Online published: 2013-11-20
Supported by
The project is supported by NSFC(11131003), 985-Project.
We consider a random walk on Z in random environment with possible jumps {−L, · · · , −1, 1}, in the case that the environment {ωi : i ∈ Z} are i.i.d.. We establish the renewal theorem for the Markov chain of “the environment viewed from the particle” in both annealed probability and quenched probability, which generalize partially the results of Kesten (1977) and Lalley (1986) for the nearest random walk in random environment on Z, respectively. Our method is based on the intrinsic branching structure within the (L, 1)-RWRE formulated in Hong and Wang (2013).
HONG Wen-Ming , SUN Hong-Yan . RENEWAL THEOREM FOR (L, 1)-RANDOM WALK IN RANDOM ENVIRONMENT[J]. Acta mathematica scientia, Series B, 2013 , 33(6) : 1736 -1748 . DOI: 10.1016/S0252-9602(13)60119-8
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