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Mathematics > Probability

arXiv:1804.08947 (math)
[Submitted on 24 Apr 2018 (v1), last revised 30 Oct 2018 (this version, v2)]

Title:Stochastic integration in quasi-Banach spaces

Authors:Petru A. Cioica-Licht, Sonja G. Cox, Mark C. Veraar
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Abstract:In this paper 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 $p\in (0,1]$. The latter is natural to consider for its potential application to adaptive wavelet methods for stochastic partial differential equations.
Subjects: Probability (math.PR); Functional Analysis (math.FA)
MSC classes: Primary: 60H05, Secondary: 46A16, 60B11
Cite as: arXiv:1804.08947 [math.PR]
  (or arXiv:1804.08947v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1804.08947

Submission history

From: Petru A. Cioica-Licht [view email]
[v1] Tue, 24 Apr 2018 10:39:45 UTC (80 KB)
[v2] Tue, 30 Oct 2018 21:11:23 UTC (81 KB)
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