caa a22 4500 445391952 CHVBK 20180317143049.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10955-011-0134-x doi (NATIONALLICENCE)springer-10.1007/s10955-011-0134-x Zucca Fabio Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy aut Survival, Extinction and Approximation of Discrete-time Branching Random Walks [Elektronische Daten] [Fabio Zucca] We consider a general discrete-time branching random walk on a countable setX. We relate local, strong local and global survival with suitable inequalities involving the first-moment 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 continuous-time case and we give some examples and counterexamples. Springer Science+Business Media, LLC, 2011 Branching random walk nationallicence Branching process nationallicence Percolation nationallicence Multitype contact process nationallicence Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/4(2011-02-01), 726-753 0022-4715 142:4<726 2011 142 10955 https://doi.org/10.1007/s10955-011-0134-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0134-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zucca Fabio Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/4(2011-02-01), 726-753 0022-4715 142:4<726 2011 142 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer