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5977概率中等数值题medium

Optional Stopping on a Product Martingale

题目

Let X_1, X_2, ... be i.i.d. fair +-1 steps and define the product P_n = prod_{i=1}^n (1 + (1/2) X_i), with P_0 = 1. Let N be any almost-surely finite stopping time. Treating P_n as a martingale, what is E[P_N]?

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