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

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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.