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September 2013 Conditional distributions and waiting times in multitype branching processes
H. K. Alexander
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Adv. in Appl. Probab. 45(3): 692-718 (September 2013). DOI: 10.1239/aap/1377868535

Abstract

In this paper we present novel results for discrete-time and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared. Specifically, both forward and backward equations for the distribution of type-specific population sizes over time, conditioned on the non\-appearance of one or more particular types, are derived. In tandem, equations for the probability that one or more particular types have not yet appeared are also derived. Brief examples illustrate numerical methods and potential applications of these results in evolutionary biology and epidemiology.

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H. K. Alexander. "Conditional distributions and waiting times in multitype branching processes." Adv. in Appl. Probab. 45 (3) 692 - 718, September 2013. https://doi.org/10.1239/aap/1377868535

Information

Published: September 2013
First available in Project Euclid: 30 August 2013

zbMATH: 1276.92081
MathSciNet: MR3102468
Digital Object Identifier: 10.1239/aap/1377868535

Subjects:
Primary: 60G99
Secondary: 92D15, 92D30

Rights: Copyright © 2013 Applied Probability Trust

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Vol.45 • No. 3 • September 2013
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