## The Annals of Probability

### Killing a Markov Process Under a Stationary Measure Involves Creation

R. K. Getoor

#### Abstract

We construct the Kuznetsov measure associated with an excessive measure, $m$, and the semigroup of a process killed according to a multiplicative functional, $M$, in terms of the Kuznetsov measure corresponding to $m$ and the original semigroup and certain functionals coming from $M$. We also obtain an explicit decomposition of $m$ into its invariant and purely excessive parts relative to the killed semigroup. This decomposition involves objects related to the fine structure of $M$ that have been introduced in recent years.

#### Article information

Source
Ann. Probab., Volume 16, Number 2 (1988), 564-585.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176991773

Digital Object Identifier
doi:10.1214/aop/1176991773

Mathematical Reviews number (MathSciNet)
MR929063

Zentralblatt MATH identifier
0651.60078

JSTOR