I am looking at an irreducible, continuous-time jump process $(X_t)_{t\geq0}$ with the following jump times. Let a Poisson process $(T_i)_{i=1}^\infty$ determine the event times. With probability $0
I know that the jump chain $(X_{J_i})_{i=1}^\infty$ is ergodic, from other parts of my work. How can I conclude that the original chain is ergodic? My intuition is that jumps still occur sufficiently frequently (because with high probability, there are at least $t/2$ events by time $t$).
Thanks for your help, Derek