Isomorphisms for spaces of predictable processes and an extension of the It\^{o} integral
Probability
2025-11-21 v1
Abstract
Our goal of this note is to give an easy proof that spaces of predictable processes with values in a Banach space are isomorphic to spaces of progressive resp. adapted, measurable processes. This provides a straightforward extension of the It\^{o} integral in infinite dimensions. We also outline an application to stochastic partial differential equations.
Cite
@article{arxiv.1907.05137,
title = {Isomorphisms for spaces of predictable processes and an extension of the It\^{o} integral},
author = {Barbara Rüdiger and Stefan Tappe},
journal= {arXiv preprint arXiv:1907.05137},
year = {2025}
}
Comments
8 pages