Consider a Markov chain Xn,n 0 whose states are the nonnegative integers. Suppose that P0,0 =
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Consider a Markov chain Xn,n ≥ 0 whose states are the nonnegative integers.
Suppose that P0,0 = 1, and let P(j) be the probability of ever entering state 0 given X0 = j . Show that P(Xn), n ≥ 0 is a Doob martingale.
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