## The Annals of Probability

### Regular Birth Times for Markov Processes

A. O. Pittenger

#### Abstract

A random time $R$ is called a regular birth time for a Markov Process if (i) the $R$-past and $R$-future are conditionally independent with respect to $X(R)$ and (ii) the post-$R$ process evolves as a Markov process, perhaps with different probability laws. In this paper we characterize each regular birth time in terms of an earlier, coterminal time $L$. It is shown (Theorem 4.2) that to the post-$L$ process $R$ appears as an optional time, perhaps with dependency on pre-$L$ information and on a certain invariant set.

#### Article information

Source
Ann. Probab., Volume 9, Number 5 (1981), 769-780.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994307

Digital Object Identifier
doi:10.1214/aop/1176994307

Mathematical Reviews number (MathSciNet)
MR628872

Zentralblatt MATH identifier
0475.60055

JSTOR