Q83·Section III (Statistics)·83 of 145A martingale remains one for its own (smaller) filtrationLet {(Xn,Fn)}n=1∞\{(X_n,\mathcal F_n)\}_{n=1}^\infty{(Xn,Fn)}n=1∞ be a martingale. Let ζn=σ(X1,X2,…,Xn)\zeta_n=\sigma(X_1,X_2,\dots,X_n)ζn=σ(X1,X2,…,Xn). Then {(Xn,ζn)}n=1∞\{(X_n,\zeta_n)\}_{n=1}^\infty{(Xn,ζn)}n=1∞ is a: OptionsAMartingaleBSub MartingaleCSuper MartingaleDWhite noisePick an option to check your answer.Show answerShow solution Report a problem with this question← Q82All questionsQ84 →Keyboard: A–D answer · S solution · ←/→ previous/next