English

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.

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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}
}

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8 pages