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Limit theorems for the numbers of rare mutants: a branching process model

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

Anthony G. Pakes
Anthony G. Pakes*
Affiliation:
University of Western Australia
*
∗Postal address: Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia.
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Abstract

We generalize a two-type mutation process in which particles reproduce by binary fission, inheriting the parental type, but which can mutate with small probability during their lifetimes to the opposite type. The generalization allows an arbitrary offspring distribution. The branching process structure of this scheme is exploited to obtain a variety of limit theorems, some of which extend known results for the binary case. In particular, practically usable asymptotic normality results are obtained when the initial population size is large.

Keywords

MUTATION PROCESSMARTINGALESPOISSON APPROXIMATION

MSC classification

Primary: 60J85: Applications of branching processes
Secondary: 60F05: Central limit and other weak theorems
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 4 , December 1992 , pp. 778 - 794
Copyright
Copyright © Applied Probability Trust 1992 

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