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Branching processes in near-critical random environments

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Peter Jagers  and
Fima Klebaner
Peter Jagers
Affiliation:
Department of Mathematical Statistics, Chalmers University of Technology, Chalmers, SE-412 96 Gothenburg, Sweden. Email address: jagers@math.chalmers.se
Fima Klebaner
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, VIC 3800, Australia. Email address: fima.klebaner@sci.monash.edu.au
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Abstract

Branching processes are studied in random environments that are influenced by the population size and approach criticality as the population gets large. Results are applied to the polymerase chain reaction (PCR), which is empirically known to exhibit first exponential and then linear growth of molecule numbers.

Keywords

Branching processrandom environmentPCR

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K37: Processes in random environments
Type
Part 1. Branching processes
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 17 - 23
Copyright
Copyright © Applied Probability Trust 2004 

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