Il giorno 4 maggio alle ore 14:30 in aula 3014 del Dipartimento di
Matematica e Applicazioni dell'Università di Milano-Bicocca, la dottoressa
Sophie Hautphenne dell'Università di Melbourne e Politecnico di Losanna,
terrà un seminario dal titolo:
The probabilities of extinction in a branching random walk on a strip
Tutti gli interessati sono invitati a partecipare.
Abstract.
We consider a class of multitype Galton-Watson branching processes with
countably infinite type set X whose mean progeny matrices have a block
lower Hessenberg form. For these processes, we derive partial and global
extinction criteria. Our approach involves embedding a finite-type
explosive Galton-Watson process in a varying environment in the original
infinite-type process, and then establishing asymptotic relationships
between the two processes. We study the probability of extinction in sets
of types A ⊆ X , q(A). In particular, we develop conditions for q(A) to be
different from the global and partial extinction probability vectors. We
present an iterative method to compute the vectors q(A), and investigate
their location in the set of fixed points of the progeny generating vector.