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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Iksanov, Alexander¹  Kabluchko, Zakhar² 

[1] Taras Shevchenko Natl Univ Kyiv, Fac Comp Sci & Cybernet, UA-01601 Kiev, Ukraine

[2] Westfalische Wilhelms Univ Munster, Inst Math Stat, D-48149 Munster, Germany

关键词: Extremal process;    Functional limit theorem;    Galton-Watson process with immigration;    Perpetuity;   

DOI  :  10.1016/j.spa.2017.04.012

来源: Elsevier

【 摘 要 】

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). (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free