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The iterated Galton–Watson process

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Boleslaw Gawel  and
Marek Kimmel
Boleslaw Gawel*
Affiliation:
Silesian University
Marek Kimmel*
Affiliation:
Rice University
*
*Postal address: Department of Mathematics, Silesian University, Katowice, Poland.
**Postal address: Department of Statistics, Rice University, PO Box 1892, Houston, TX 77251, USA.
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Abstract

We consider the mathematical properties of a time-discrete stochastic process describing explosive proliferation of DNA repeats in human genetic diseases. The process is constructed using a cascade of Galton–Watson branching processes. The main results concern the probability of absorption and the supergeometric growth of the process in the supercritical case. Examples of simulations are provided.

Keywords

GALTON–WATSON PROCESSDNA

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 949 - 959
Copyright
Copyright © Applied Probability Trust 1996 

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