Intrinsic branching structure within random walk on $\mathbb{Z}$

Abstract

In this paper, we reveal the branching structure for a non-homogeneous random walk with bounded jumps. The ladder time $T_1,$ the first hitting time of $[1,\infty )$ 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.

26 pages; 7 figures; 1 table

References in corpus (1)

• Branching structure for an (L-1) random walk in random environment and its applications