This is an announcement for the paper "Stochastic integration in UMD Banach spaces" by Jan van Neerven, Mark Veraar, Lutz Weis.
Abstract: In this paper we construct a theory of stochastic integration of processes with values in $\calL(H,E)$, where $H$ is a separable Hilbert space and $E$ is a UMD Banach space. The integrator is an $H$-cylindrical Brownian motion. Our approach is based on a two-sided $L^p$-decoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic integration of $\calL(H,E)$-valued functions introduced recently by two of the authors. We obtain various characterizations of the stochastic integral and prove versions of the It^o isometry, the Burkholder-Davis-Gundy inequalities, and the representation theorem for Brownian martingales.
Archive classification: Probability; Functional Analysis
Mathematics Subject Classification: 60H05; 28C20; 60B11
Remarks: To appear in the Annals of Probability
The source file(s), Paper_vanNeerven_Veraar_Weis.tex: 112246 bytes, is(are) stored in gzipped form as 0610619.gz with size 32kb. The corresponding postcript file has gzipped size 138kb.
Submitted from: m.c.veraar@tudelft.nl
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