stochastically closed set

by Marso   Last Updated August 14, 2019 15:20 PM

In p-286, in a book named Elementary Probability Theory with Stochastic Processesby K.L Chung, he defined a set of states is called stochastically closed iff starting from any state in the set the particle will remain forever in the set.

May I ask whether the definition is applicable for Markov chain on metric space also? Is there any relation between stochastically closed set and topologically closed set? Thanks for any sort of help.

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