Law of large numbers for random walk with unbounded jumps and BDP with bounded jumps in random environment

2014/06/24 by Huaming Wang, Hua-Ming Wang, Wang, Hua-Ming
Mathematics · #60J80 #60K37 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60J80 #msc:60K37

paper · pdf · doi:10.48550/arxiv.1406.6222

25 pages

openalex publication_date 2014/06/24 · arxiv created 2014/09/28 · arxiv updated 2014/09/30 · openalex created_date 2016/10/14 · openalex updated_date 2026/07/28

Abstract

We study random walk with unbounded jumps in random environment. The environment is stationary and ergodic, uniformly elliptic and decays polynomially with speed Dj^-(3+ε₀) for some small ε₀>0 and proper D>0. We prove a law of large number with positive velocity under the condition that the annealed mean of the hitting time of the positive half lattice is finite. Secondly, we consider birth and death process with bounded jumps in stationary and ergodic environment. Under the uniformly elliptic condition, we prove a law of large number and give the explicit formula of its velocity.

Citations

• Birth and death process with one-side bounded jumps in random environment

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