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Survival probabilities and extinction times for some multitype branching processes

Published online by Cambridge University Press:  01 July 2016

Edward Pollak*
Affiliation:
Iowa State University, Ames

Abstract

This paper deals with the computation of survival probabilities and extinction times for multitype positively regular branching processes. If all of the generating functions of the offspring distributions are of the linear fractional form and have the same denominator, explicit expressions may be obtained for all of their iterates. It is then possible to obtain formulae for survival probabilities and bounds on the mean time to extinction, given extinction, of a line descended from a single individual. If there are two types and the offspring distributions are bivariate Poisson, their generating functions may be bounded by linear fractional generating functions. It is then possible to compute upper and lower bounds on mean times to extinction, given extinction, and this is done for some special cases.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1974 

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