Question

For the random walk of Example 4.18, use the strong law of large numbers to give another proof that the Markov chain is transient when p [Hint: Note that the state at time n can be written as Σίι Yi, where the Y's are independent and PO-1)-p-1-PY,--1). Argue that if p 〉 흘, then, by the strong law of large numbers. Ση-1 Ý, oo as n oo and hence the initial state 0 can be visited only finitely often, and hence must be transient. A similar argument holds when p < .

Answer 1

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