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April, 1988 Random Time Changes for Processes with Random Birth and Death
H. Kaspi
Ann. Probab. 16(2): 586-599 (April, 1988). DOI: 10.1214/aop/1176991774


We study a random time change for stationary Markov processes $(Y_t, Q)$ with random birth and death. We use an increasing process, obtained from a homogeneous random measure (HRM) as our clock. We construct a time change that preserves both the stationarity and the Markov property. The one-dimensional distribution of the time-changed process is the characteristic measure $\nu$ of the HRM, and its semigroup $(\tilde{P}_t)$ is a naturally defined time-changed semigroup. Properties of $\nu$ as an excessive measure for $(\tilde{P}_t)$ are deduced from the behaviour of the HRM near the birth time. In the last section we apply our results to a simple HRM and connect the study of $Y$ near the birth time to the classical Martin entrance boundary theory.


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H. Kaspi. "Random Time Changes for Processes with Random Birth and Death." Ann. Probab. 16 (2) 586 - 599, April, 1988.


Published: April, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0651.60074
MathSciNet: MR929064
Digital Object Identifier: 10.1214/aop/1176991774

Primary: 60J55
Secondary: 60J45 , 60J50

Keywords: additive functional , characteristic measure , excessive measure , homogeneous random measure , Markov processes , Ray-Knight compactification , Time change

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 2 • April, 1988
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