The probabilities of extinction in a branching random walk on a strip [article]

Peter Braunsteins, Sophie Hautphenne
2019 arXiv   pre-print
We consider a class of multitype Galton-Watson branching processes with a countably infinite type set X_d whose mean progeny matrices have a block lower Hessenberg form. For these processes, the probability q(A) of extinction in subsets of types A⊆X_d may differ from the global extinction probability q and the partial extinction probability q̃. After deriving partial and global extinction criteria, we develop conditions for q<q(A)<q̃. We then present an iterative method to compute the vector
more » ... ) for any set A. Finally, we investigate the location of the vectors q(A) in the set of fixed points of the progeny generating vector.
arXiv:1805.07634v2 fatcat:pwzf77u5tbhbpjhdpc5vq2yfji