Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 23 octobre 2019 à 11h10 en Amphi Darwin, Alexander Iksanov nous parlera de : Functional limit theorems for divergent perpetuities and Galton-Watson processes with very active immigration

Résumé : I am going to discuss weak convergence in the Skorokhod space of Galton-Watson processes with immigration (GWI), properly normalized, under the assumption that the tail of the immigration distribution has a logarithmic decay. It will be explained that the limits are extremal shot noise processes. Interestingly, both the behavior in mean and the survival probability (especially in the subcritical case) of the underlying Galton-Watson processes without immigration affect the asymptotics in question. The sequence of the conditional expectations of GWI given the immigration forms a very particular instance of a (divergent) perpetuity. In view of this I shall also present functional limit theorems in the Skorokhod space for general divergent perpetuities and suprema of perturbed random walks which are closely related objects.

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