Codice  QDD 63 
Titolo  Survival, extinction and approximation of discretetime branching random walks 
Data  20100325 
Autore/i  Zucca, F. 
Link  Download full text 
Abstract  We consider a general discretetime branching random walk on a countable set X. We relate local and global survival with suitable inequalities involving the firstmoment matrix M of the process. In particular we prove that, while the local behavior is characterized by M, the global
behavior cannot be completely described in terms of properties involving M alone. Moreover we show that locally surviving branching random walks can be approximated by sequences of spatially confined and stochastically dominated branching random walks which eventually survive locally if the (possibly finite) state space is large enough. An analogous result can be achieved by
approximating a branching random walk by a sequence of multitype contact processes and allowing a sufficiently large number of particles per site. We compare these results with the ones obtained in the continuoustime case and we give some examples and counterexamples. 
