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

Felix Hermann and Peter Pfaffelhuber

Stochastic Processes and their Applications, 2020, vol. 130, issue 4, 2488-2518

Abstract: 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.

Keywords: Piecewise deterministic Markov process; Branching process; Branching process with disasters; Duality of Markov processes; Extinction probability; Survival probability (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414919300110
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:4:p:2488-2518

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2019.07.011

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().