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{ X n } is an irreducible discrete-time Markov chain, with state space S, transition matrix P { Y n } is an irreducible discrete-time

{Xn } is an irreducible discrete-time Markov chain, with state space S, transition matrix P

{Yn } is an irreducible discrete-time Markov chain, with state space S, transition matrix M such at at each step Yn will follow P at probability pi and stay with probability 1-pi . (Mij=piPij, Mii=piPii+1pi ) where 0<pi<1.

If Xn is positive recurrent/has a stationary distribution. Is Yn the same?

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