As in problem 4 in sect101 let x1 x2 be iid real random, Ask an Expert

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As in Problem 4 in §10.1, let X1, X2,... , be i.i.d. real random variables with E |X1| ∞. Let Sn := X1 +· · · + Xn . For n = 1, 2,... , let T-n := Sn/n. Let B-n be the smallest σ-algebra for which Sk are measurable for all k ≥ n. Show that {Tk, Bk }k≤-1 is a reversed martingale and {|Tk |, Bk }k≤-1 is a reversed submartingale.

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