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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, the chain does nothing. Else, with probability $1-p$, it moves somewhere giving a jump time $J_i$. Thus $T_i\leq J_i$ for all $i$.

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

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    Hi Mike, thanks $f$or pointing me in the right direction. Think I've got it!2012-05-09

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