2010/03/19 by Wenming Hong, Huaming Wang, Hong, Wenming +1 · 2 citations
Decision Sciences · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1003.3731
31 pages
arxiv created 2010/03/19 · openalex publication_date 2010/03/19 · arxiv updated 2010/03/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching structure. Firstly, we specify the explicit invariant density by a method different with the one used in Brémont [3] and reprove the law of large numbers of the random walk by a method known as the environment viewed from particles". Secondly, the branching structure enables us to prove a stable limit law, generalizing the result of Kesten-Kozlov-Spitzer [11] for the nearest random walk in random environment. As a byproduct, we also prove that the total population of a multitype branching process in random environment with immigration before the first regeneration belongs to the domain of attraction of some κ-stable law.