## The Annals of Probability

### Applications of Duality to a Class of Markov Processes

Diane L. Schwartz

#### Abstract

Let $S$ be a countable set and let $\xi_t$ be a Markov process on the subsets of $S$. Harris has given criteria for the existence of a dual process $\xi_t^\ast$ on the finite subsets of $S$. By extending Harris's notion of duality the class of $\xi_t$ which have dual processes is enlarged. The dual processes are then used to study the ergodic behavior of $\xi_t$. Also treated is a class of $\xi_t$ which have growing dual processes.

#### Article information

Source
Ann. Probab., Volume 5, Number 4 (1977), 522-532.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995758

Digital Object Identifier
doi:10.1214/aop/1176995758

Mathematical Reviews number (MathSciNet)
MR448631

Zentralblatt MATH identifier
0367.60111

JSTOR