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Birth and death on a Brownian flow: a Feller semigroup and its generator and a martingale problem

Published online by Cambridge University Press:  14 July 2016

Michael J. Phelan
Michael J. Phelan*
Affiliation:
University of Pennsylvania
*
∗Postal address: Department of Statistics, The Wharton School of the University of Pennsylvania, 3000 Steinberg Hall-Dietrich Hall, Philadelphia, PA 19104–6302, USA.
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Abstract

We consider a system of particles in birth and death on a stochastic flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of bounded counting measures. We show that its transition semigroup is a Feller semigroup and exhibit its pregenerator. The pregenerator defines a martingale problem. We show that the particle process solves the problem uniquely.

Keywords

BROWNIAN FLOWPOISSON PROCESSFELLER SEMIGROUPMARTINGALE PROBLEM
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 71 - 87
Copyright
Copyright © Applied Probability Trust 1996 

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