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I'm given a Markov chain [itex]Q_k[/itex], k>0 with stationary transition probabilities. The state is space uncountable.

What I want to show is that the chain is asymptotically stationary, that is it converges in distribution to some random variable Q.

All I have at hand is an k-independent upper bound for [itex]P(|Q_k|>x)[/itex] for all x in the state space (and some indecomposability assumptions on the state space).

Is this enough to conclude convergence of the chain?

Thanks for any help.

-Pere

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# Stationary distribution of Markov chain

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