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Q82Section III (Statistics)82 of 145

Doob's martingale E(Z∣Fn)E(Z\mid F_n)

Suppose Z is an integrable random variable on (Ω,F,P)(\Omega,F,P) and FnF_n are non-decreasing σ\sigma-fields in F. Let Xn=E(Z∣Fn)X_n=E(Z\mid F_n). Then E(Xn+1∣Fn)=E(X_{n+1}\mid F_n)=

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