Malliavin calculus and decoupling inequalities in Banach spaces

Details Malliavin calculus and decoupling inequalities in Banach spaces Malliavin calculus and decoupling inequalities in Banach spaces

2008-01-18

arxiv.org/abs/0801.2899v2

Mathematics

Functional Analysis

17 pages

Scientific paper

We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banach spaces. In the white noise case we obtain two sided L^p-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-Ito chaoses. Our main tools are decoupling inequalities for vector-valued random variables. In the opposite direction we use Meyer's inequalities to give a new proof of a decoupling result for Gaussian chaoses in UMD Banach spaces.

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