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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 11, Fasc. 1,
pages 1 - 17
 

COMPLEMENTS ON DECOUPLING INEQUALITIES FOR MULTILINEAR FUNCTIONS IN STABLE RANDOM VECTORS

Balram S. Rajput
Jan Rosinski

Abstract: Let B and V be real separable Banach spaces and d be a positive integer. Let M  : Bd --> V be a measurable symmetric multilinear function, and let X be a B -valued symmetric p -stable random vector. It is shown that if 0 < q < p/2, then the finiteness of E ||M (X,...,X) ||q
               V  is not sufficient for the validity of the important part of the decoupling inequalities. A natural condition, in terms of the spectral measure of X and an algebraic equation involving M, is proposed and it is proved that this condition ensures decoupling inequalities for all q  (-  (0,p). This result complements de Acosta’s decoupling inequalities for multilinear functions in B -valued symmetric p -stable random vectors.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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