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Disjointification of martingale differences and conditionally independent random variables with some applications

Sergey AstashkinFedor SukochevChin Pin Wong — 2011

Studia Mathematica

Disjointification inequalities are proven for arbitrary martingale difference sequences and conditionally independent random variables of the form f k ( s ) x k ( t ) k = 1 , where f k ’s are independent and xk’s are arbitrary random variables from a symmetric space X on [0,1]. The main results show that the form of these inequalities depends on which side of L₂ the space X lies on. The disjointification inequalities obtained allow us to compare norms of sums of martingale differences and non-negative random variables with...

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