Functional limit theorems for Galton-Watson processes with very active immigration

Alexander Iksanov; Zakhar Kabluchko

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arXiv · 1612.01573

Functional limit theorems for Galton-Watson processes with very active immigration

Alexander Iksanov·Zakhar Kabluchko

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Abstract

We prove weak convergence on the Skorokhod space of Galton-Watson processes with immigration, properly normalized, under the assumption that the tail of the immigration distribution has a logarithmic decay. The limits are extremal shot noise processes. By considering marginal distributions, we recover the results of Pakes [Adv. Appl. Probab., 11(1979), 31--62].

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Alexander Iksanov, Zakhar Kabluchko. 2016-12-05. Functional limit theorems for Galton-Watson processes with very active immigration. https://arxiv.org/abs/1612.01573

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