One-Dimensional Branching Random Walk in a Random Environment: a Classification

#### F. Comets, M.V. Menshikov, S.Yu. Popov

1998, v.4, №4, 465-477

ABSTRACT

We consider a supercritical branching random walk on ${\ Z}_+$ in a one-dimensional independent, homogeneous random environment, which enters both the branching mechanism and the step transition. We introduce an appropriate classification and we prove some transience and recurrence criteria.

Keywords: branching random walk,Lyapunov function,random environment