# Neat definition of Harris Ergodicity

I can't find any reference where the definition of Harris Ergodicity for Continuous time Markov processes is defined.

a) What would be exactly the definition?

b) What reference could be helpful?

EDIT: From what I've read From "Applied Probability and Queues(pg. 198-200)"(Asmussen) I understand that $(X(t))$ is Harris Ergodic if it has a regeneration set (a generalisation of a positive recurrent state) and an invariant distribution.

Is it true that if an embedded chain from $(X(t))$ is Harris ergodic then $(X(t))$ itself is Harris Ergodic?

• Did you check Meyn, Tweedie, Stability of Markovian processes II: Continuous-time processes and sampled chains? – Joris Bierkens Mar 21 '16 at 18:46

A continuous time Markov process $X$ is Harris recurrent provided there exists a $\sigma$-finite measure $\mu$ on the state space $S$ of $X$ such that for all Borel sets $B\subset S$, if $\mu(B)>0$ then $\Bbb P^x(\int_0^\infty 1_B(X_t)\,dt=\infty)=1$ for all $x\in S$. See Mesure invariante sur les classes récurrentes des processus de Markov by Azéma, Kaplan-Duflo, and Revuz, D. in Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 8 (1967) 157–181. They use the fact that an associated embedded chain is Harris recurrent in the discrete time sense.