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

Alexander Iksanov and Zakhar Kabluchko

Stochastic Processes and their Applications, 2018, vol. 128, issue 1, 291-305

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 (1979).

Keywords: Extremal process; Functional limit theorem; Galton–Watson process with immigration; Perpetuity (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spa.2017.04.012

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