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A Girsanov transformation for birth and death on a Brownian flow

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 Brownian 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 counting measures. The system depends on a handful of parameters including a rate of drift, diffusion, birth, and killing. We exhibit a Girsanov formula for the absolutely continuous change of particle system by way of a change of drift, birth, and killing rates. We can only allow for a restrictive change of drift on the flow, but for fairly unrestrictive change of birth and death rates. The result is therefore of some interest in problems of statistical inference from passive transport of transient tracers.

Keywords

BROWNIAN FLOWPOISSON PROCESSGIRSANOV FORMULA
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 88 - 100
Copyright
Copyright © Applied Probability Trust 1996 

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