Question: Let (Sn) be the simple random walk, that is, Sn = So + Xit ... + Xn where X1, X2, ... are iid random variables

Let (Sn) be the simple random walk, that is, Sn = So + Xit ... + Xn where X1, X2, ... are iid random variables with P [X1 = 1] = P [X1 = -1] = ?. (i) Let T be the first time that the walk hits 0 or m. Using that (Sn)n, (Sh -n)n, and (Sn - 3nSn)n are martingales, show that for all 0

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