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Stochastic integration in quasi-Banach spaces

Journal Article (2023)
Author(s)

Petru A. Cioica-Licht (University of Kassel)

Sonja G. Cox (Korteweg-de Vries Institute for Mathematics)

M.C. Veraar (TU Delft - Analysis)

Research Group
Analysis
DOI related publication
https://doi.org/10.4064/sm180424-31-10
More Info
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Publication Year
2023
Language
English
Research Group
Analysis
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. @en
Issue number
1
Volume number
269
Pages (from-to)
1-64
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Abstract

We develop a stochastic integration theory for processes with values in a quasi-Banach space. The integrator is a cylindrical Brownian motion. The main results give sufficient conditions for stochastic integrability. They are natural extensions of known results in the Banach space setting. We apply our main results to the stochastic heat equation where the forcing terms are assumed to have Besov regularity in the space variable with integrability exponent p ∈ (0, 1]. The latter is natural to consider for its potential application to adaptive wavelet methods for stochastic partial differential equations.

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