@article{90e2eadd79854f878b7cd215f8060ab9,
title = "Cylindrical continuous martingales and stochastic integration in infinite dimensions",
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. ",
keywords = "cylindrical martingale, quadratic variation, continuous local martingale, stochastic integration in Banach spaces, UMD Banach spaces, Burkholder-Davis-Gundy, random time change, -radonifying operators, inequalities, It{\^o} formula, stochastic evolution equation, stochastic convolution, Functional calculus",
author = "Mark Veraar and Ivan Yaroslavtsev",
year = "2016",
doi = "10.1214/16-EJP7",
language = "English",
volume = "21",
pages = "1--53",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",
number = "59",
}