## The Annals of Probability

### Birth, Death and Conditioning of Markov Chains

#### Abstract

Given a Markov chain with stationary transition probabilities, we study random times $\tau$ determined by the evolution of the Markov chain for which either the pre-$\tau$ or post-$\tau$ process is Markovian with stationary transition probabilities. A complete description is given of all such random times which admit a conditional independence property analogous to the strong Markov property at a stopping time.

#### Article information

Source
Ann. Probab., Volume 5, Number 3 (1977), 430-450.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995803

Digital Object Identifier
doi:10.1214/aop/1176995803

Mathematical Reviews number (MathSciNet)
MR445613

Zentralblatt MATH identifier
0363.60052

JSTOR