Can someone recommend me where can I find examples in which we can apply Krylov-Bogoliubov Theorem and examples in which we can not apply this theorem?
P.S. I mean Krylov - Bogoliubov Theorem for continuous Markov processes.
Thank you!
Applications of Krylov-Bogoliubov Theorem
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stochastic-processes
dynamical-systems
markov-process
1 Answers
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I wonder whether your interest comes from ergodic theory. If so, you can have a look say at Walter's ergodic theory book. The prototype of an example comes from iterating a continuous map on a compact metric space.
Otherwise, look at http://www.hairer.org/notes/Convergence.pdf for a typical counterexample, and for an example consider a compact Polish space.
Incidentally, it is peculiar to call an operator "Markov" before knowing whether it is really Markov, but it is something apparently usual in stochastic processes.