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Jump-type Fleming-Viot processes

Part of: Special processes Markov processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Seiji Hiraba
Seiji Hiraba*
Affiliation:
Osaka City University
*
∗ Postal address: Department of Mathematics, Graduate School of Science, Osaka City University, Sugimoto-3, Sumiyoshi-ku, Osaka 558-8585, Japan. Email address: hiraba@sci.osaka-cu.ac.jp
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Abstract

In 1991 Perkins [7] showed that the normalized critical binary branching process is a time inhomogeneous Fleming-Viot process. In the present paper we extend this result to jump-type branching processes and we show that the normalized jump-type branching processes are in a new class of probability measure-valued processes which will be called ‘jump-type Fleming-Viot processes’. Furthermore we also show that by using these processes it is possible to introduce another new class of measure-valued processes which are obtained by the combination of jump-type branching processes and Fleming-Viot processes.

Keywords

Measure-valued processbranching processFleming-Viot processbranching particle systemMoran particle systemmartingale problemconvergence in distribution

MSC classification

Primary: 60G57: Random measures 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Secondary: 60J75: Jump processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory 92D10: Genetics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 1 , March 2000 , pp. 140 - 158
Copyright
Copyright © Applied Probability Trust 2000 

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References

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