Author： Veraar Mark
Publisher： Taylor & Francis Ltd
ISSN： 1744-2508
Source： Stochastics: An International Journal of Probability and Stochastic Processes, Vol.79, Iss.6, 2007-12, pp. : 601-618
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Abstract
Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator is an arbitrary real-valued continuous local martingale. We give several characterizations of integrability and prove a version of the Itô isometry, the Burkholder-Davis-Gundy inequality, the Itô formula and the martingale representation theorem.
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