Multi-type branching processes with time-dependent branching rates

Under mild nondegeneracy assumptions on branching rates in each generation, we provide a criterion for almost sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total number of particles (conditioned on survival and divided by t...

Full description

Saved in:
Bibliographic Details
Published in:Journal of applied probability 2018-09, Vol.55 (3), p.701-727
Main Authors: Dolgopyat, D., Hebbar, P., Koralov, L., Perlman, M.
Format: Article
Language:English
Subjects:
Conditioning
Criteria
Random variables
Research Papers
Time dependence
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Under mild nondegeneracy assumptions on branching rates in each generation, we provide a criterion for almost sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total number of particles (conditioned on survival and divided by the expectation of the resulting random variable) to approach an exponential random variable as time goes to ∞.
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2018.46