Question: 4. Consider a Markov chain on the set S = {0, 1, 2, . . . } with transition probabilities pi,i+1 = ai , pi,0

4. Consider a Markov chain on the set S = {0, 1, 2, . . . } with transition probabilities pi,i+1 = ai , pi,0 = 1 − ai , where (ai : i ≥ 0) is a sequence of constants satisfying 0 < ai < 1 for all i . Let b0 = 1 and bi = a0a1 · · · ai−1 for i ≥ 1. Show that the chain is

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