THE PROBABILITIES OF EXTINCTION IN A BRANCHING RANDOM WALK ON A STRIP

Abstract

We consider a class of multitype Galton-Watson branching processes with a countably infinite type set whose mean progeny matrices have a block lower Hessenberg form. For these processes, we study the probabilities of extinction in sets of types. We compare with the global extinction probability, that is, the probability that the population eventually becomes empty, and with the partial extinction probability, that is, the probability that all types eventually disappear from the population. After deriving partial and global extinction criteria, we develop conditions for <[CDATA[ textbf{textit{q}} < textbf{textit{q}}(A). We then present an iterative method to compute the vector for any set A. ..