Let 1 , 2 , ... be i.i.d. r.v.s with zero mean and variance
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Let ξ1, ξ2, ... be i.i.d. r.v.’s with zero mean and variance σ2 > 0, S0 = 0, St = ξ1+...+ξt for t = 0,1, .... Show that Xt = S2t −σ2t is a martingale with respect to ξt.
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