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Birth and death processes as projections of higher-dimensional Poisson processes

Part of: Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Nancy Lopes Garcia
Nancy Lopes Garcia*
Affiliation:
Universidade Estadual de Campinas
*
* Postal address: Departamento de Estatística, IMECC, Cidade Universitária ‘Zeferino Vaz', Caixa Postal 6065, 13.081-970, Campinas, SP, Brazil.
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Abstract

Birth and death processes can be constructed as projections of higher-dimensional Poisson processes. The existence and uniqueness in the strong sense of the solutions of the time change problem are obtained. It is shown that the solution of the time change problem is equivalent to the solution of the corresponding martingale problem. Moreover, the processes obtained by the projection method are ergodic under translations.

Keywords

POISSON POINT PROCESSSPATIAL BIRTH AND DEATH PROCESSESRANDOM TIME CHANGEMARTINGALE PROBLEMSPATIAL ERGODICITY

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 4 , December 1995 , pp. 911 - 930
Copyright
Copyright © Applied Probability Trust 1995 

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