Abstract of a paper by Jan van Neerven, Mark Veraar, Lutz Weis
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.PR/0610619 or http://arXiv.org/abs/math.PR/0610619 or by email in unzipped form by transmitting an empty message with subject line uget 0610619 or in gzipped form by using subject line get 0610619 to: math@arXiv.org.
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Dale Alspach