The Annals of Probability

Random Time Changes for Processes with Random Birth and Death

H. Kaspi

Full-text: Open access


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.

Article information

Ann. Probab., Volume 16, Number 2 (1988), 586-599.

First available in Project Euclid: 19 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 60J55: Local time and additive functionals
Secondary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60J50: Boundary theory

Markov processes time change homogeneous random measure additive functional excessive measure characteristic measure Ray-Knight compactification


Kaspi, H. Random Time Changes for Processes with Random Birth and Death. Ann. Probab. 16 (1988), no. 2, 586--599. doi:10.1214/aop/1176991774.

Export citation