## The Annals of Probability

### A Path Decomposition for Markov Processes

P. W. Millar

#### Abstract

Let $X = \{X_t, t > 0\}$ be a right continuous strong Markov process with state space $E$; let $f$ be a continuous real valued function on $E \times E$; and let $M$ be the time at which the process $\{f(X_{t-}, X_t)\}$ achieves its (last) ultimate minimum. Then conditional on $X_M$ and the value of this minimum, the process $\{X_{M + t}\}$ is Markov and (conditionally) independent of events before $M$.

#### Article information

Source
Ann. Probab., Volume 6, Number 2 (1978), 345-348.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995581

Digital Object Identifier
doi:10.1214/aop/1176995581

Mathematical Reviews number (MathSciNet)
MR461678

Zentralblatt MATH identifier
0379.60070

JSTOR