Print Email Facebook Twitter Cylindrical continuous martingales and stochastic integration in infinite dimensions Title Cylindrical continuous martingales and stochastic integration in infinite dimensions Author Veraar, M.C. (TU Delft Analysis) Yaroslavtsev, I.S. (TU Delft Analysis) Date 2016 Abstract In this paper we define a new type of quadratic variation for cylindrical continuous local martingales on an infinite dimensional spaces. It is shown that a large class of cylindrical continuous local martingales has such a quadratic variation. For this new class of cylindrical continuous local martingales we develop a stochastic integration theory for operator valued processes under the condition that the range space is a UMD Banach space. We obtain two-sided estimates for the stochastic integral in terms of the γ-norm. In the scalar or Hilbert case this reduces to the Burkholder-Davis-Gundy inequalities. An application to a class of stochastic evolution equations is given at the end of the paper. Subject cylindrical martingalequadratic variationcontinuous local martingalestochastic integration in Banach spacesUMD Banach spacesBurkholder-Davis-Gundyrandom time change-radonifying operatorsinequalitiesItô formulastochastic evolution equationstochastic convolutionFunctional calculus To reference this document use: http://resolver.tudelft.nl/uuid:90e2eadd-7985-4f87-8b7c-d215f8060ab9 DOI https://doi.org/10.1214/16-EJP7 ISSN 1083-6489 Source Electronic Journal of Probability, 21 (59), 1-53 Part of collection Institutional Repository Document type journal article Rights © 2016 M.C. Veraar, I.S. Yaroslavtsev Files PDF 10677573.pdf 869.32 KB Close viewer /islandora/object/uuid:90e2eadd-7985-4f87-8b7c-d215f8060ab9/datastream/OBJ/view