Branching Markov Chains: Qualitative Characteristics

#### M.V. Menshikov, S.E. Volkov

1997, v.3, №2, 225-241

ABSTRACT

In this paper we study random walks with branching. We introduce the notion of recurrence and transience for these processes and provide criteria for them. For the Lamperti problem and many-dimensional random walks with branching we find the critical (for transience vs. recurrence) speed of decay of the average number of off-springs at a point with respect to its distance to the origin.

Keywords: branching random walk,Lamperti problem,recurrence,moment generating function,Lyapunov function