Weak characterizations of stochastic integrability and Dudley's theorem in infinite dimensions
Probability
2013-01-31 v2 Functional Analysis
Abstract
In this paper we consider stochastic integration with respect to cylindrical Brownian motion in infinite dimensional spaces. We study weak characterizations of stochastic integrability and present a natural continuation of results of van Neerven, Weis and the second named author. The limitation of weak characterizations will be demonstrated with a nontrivial counterexample. The second subject treated in the paper addresses representation theory for random variables in terms of stochastic integrals. In particular, we provide an infinite dimensional version of Dudley's representation theorem for random variables and an extension of Doob's representation for martingales.
Keywords
Cite
@article{arxiv.1205.5438,
title = {Weak characterizations of stochastic integrability and Dudley's theorem in infinite dimensions},
author = {Martin Ondrejat and Mark Veraar},
journal= {arXiv preprint arXiv:1205.5438},
year = {2013}
}
Comments
To appear in Journal of Theoretical Probability