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.
Publié le : 1988-04-14
Classification:
Markov processes,
time change,
homogeneous random measure,
additive functional,
excessive measure,
characteristic measure,
Ray-Knight compactification,
60J55,
60J45,
60J50
@article{1176991774,
author = {Kaspi, H.},
title = {Random Time Changes for Processes with Random Birth and Death},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 586-599},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991774}
}
Kaspi, H. Random Time Changes for Processes with Random Birth and Death. Ann. Probab., Tome 16 (1988) no. 4, pp. 586-599. http://gdmltest.u-ga.fr/item/1176991774/