Abstract

Let X be a (quasi-)Banach space. Let d = (dn)n 1 be an X-valued sequence of random variables adapted to a ltration ( Fn)n 1 on a probability space ( ;A;P), dene F1 := (Fn : n 1) and let e = (en)n 1 be aF1-conditionally independent sequence on ( ;A;P) such that L(dnjFn 1) =L(enjF1) for all n 1 (F0 =f ;?g). If there exists a p2 (0;1) and a constant Dp independent of d and e such that one has, for all n 1, X k=1 dk p D pE n X k=1 ek p

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