Suppose that {Xn:n 2 0} is a finite Markov chain with the state space S= {1,..., M}, when M is a positive integer (M < 00). Prove that there can be no null recurrent states in the chain. (Hint: Consider the cases (i) S is irreducible and (ii) S is reducible.)

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Suppose that {Xn:n 2 0} is a finite Markov chain with the state space S= {1,..., M}, when M is
a positive integer (M < 00). Prove that there can be no null recurrent states in the chain. (Hint:
Consider the cases (i) S is irreducible and (ii) S is reducible.)
Transcribed Image Text:Suppose that {Xn:n 2 0} is a finite Markov chain with the state space S= {1,..., M}, when M is a positive integer (M < 00). Prove that there can be no null recurrent states in the chain. (Hint: Consider the cases (i) S is irreducible and (ii) S is reducible.)
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