2010/12/03 by Wenming Hong, Huaming Wang, Hong, Wenming +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Primary 60J80 #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60G50 #msc:60J80 #secondary 60G50
paper · pdf · doi:10.48550/arxiv.1012.0636
26 pages; 7 figures; 1 table
arxiv created 2010/12/03 · openalex publication_date 2010/12/03 · arxiv updated 2010/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we reveal the branching structure for a non-homogeneous random walk with bounded jumps. The ladder time T1, the first hitting time of [1,∞) by the walk starting from 0, could be expressed in terms of a non-homogeneous multitype branching process. As an application of the branching structure, we prove a law of large numbers of random walk in random environment with bounded jumps and specify the explicit invariant density for the Markov chain of ``the environment viewed from the particle" .The invariant density and the limit velocity could be expressed explicitly in terms of the environment.