Markov branching processes with disasters: Extinction, survival and duality to p-jump processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Hermann, Felix¹  Pfaffelhuber, Peter² 

[1] Tech Univ Berlin, Berlin, Germany

[2] Albert Ludwigs Univ Freiburg, Freiburg, Germany

关键词: Piecewise deterministic Markov process;    Branching process;    Branching process with disasters;    Duality of Markov processes;    Extinction probability;    Survival probability;   

DOI  :  10.1016/j.spa.2019.07.011

来源: Elsevier

【 摘 要 】

A p-jump process is a piecewise deterministic Markov process with multiplicative jumps by a factor of p. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting results for the survival probabilities of time-homogeneous branching processes with arbitrary offspring distributions, underlying binomial disasters. Extending this method, we obtain corresponding results for time-inhomogeneous birth-death processes underlying time-dependent binomial disasters and continuous state branching processes with p-jumps. (C) 2019 Elsevier B. V. All rights reserved.

【 授权许可】

Free