Let X n be a discrete time Markov chain Remember that, by definition, p (n) ii P(X n i X 0 i) Show that state i is recurrent if and only if () Pu n 1...

Definitions Piin The probability of returning to state i in n steps given that the process starts i ...

Let X n be a discrete-time Markov chain. Remember that, by definition, p (n) ii = P(X

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Let X_n be a discrete-time Markov chain. Remember that, by definition, p⁽ⁿ⁾_ii = P(X_n = i|X₀ = i). Show that state i is recurrent if and only if () Pu = . n=1

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Introduction To Probability Statistics And Random Processes

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Authors: Hossein Pishro-Nik

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Let X n be a discrete-time Markov chain. Remember that, by definition, p (n) ii = P(X

Question:

(η) Σ Pu = ∞. n=1

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Introduction To Probability Statistics And Random Processes

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