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Mathematics > Probability

arXiv:1405.0075 (math)
[Submitted on 1 May 2014]

Title:A note on space-time Holder regularity of mild solutions to stochastic Cauchy problems in Lp-spaces

Authors:Rafael Serrano
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Abstract:This paper revisits the Hölder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces $L^p(\mathcal{O}),$ with $p\geq 2$ and $\mathcal{O}\subset\mathbb{R}^d$ a bounded domain. We find conditions on $p, \beta$ and $\gamma$ under which the mild solution has almost surely trajectories in $\mathcal{C}^\beta([0,T];\mathcal{C}^\gamma(\bar{\mathcal{O}})).$ These conditions do not depend on the Cameron-Martin Hilbert space associated with the driving cylindrical noise. The main tool of this study is a regularity result for stochastic convolutions in M-type 2 Banach spaces by Z. Brzeźniak (Stoch. Stoch. Rep. Vol. 61, Iss. 3-4, 1997).
Subjects: Probability (math.PR)
MSC classes: Primary 60H15, secondary 47D06, 35R15
Report number: BJPS245
Cite as: arXiv:1405.0075 [math.PR]
  (or arXiv:1405.0075v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1405.0075

Submission history

From: Rafael Serrano [view email]
[v1] Thu, 1 May 2014 01:29:14 UTC (33 KB)
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