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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
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.
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- Copyright © Applied Probability Trust 1996
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