Show that state i is also recurrent

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Reference no: EM13909244

(Renewal theory proof that a class is all recurrent or all transient) Assume that state j in a countable-state Markov chain is recurrent and i communicates with j. More specifically, assume that there is a path of length m from i to j and one of length k from j to i.

(a) Show that for any n > 0, Pm+n+k ≥ Pm Pn Pk .

(b) By summing over n, show that state i is also recurrent. Hint: Use Theorem 6.2.6.

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

Reference no: EM13909244

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