- #1
Pere Callahan
- 586
- 1
Hi all,
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
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