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November 2015 A note on space–time Hölder regularity of mild solutions to stochastic Cauchy problems in $L^{p}$-spaces
Rafael Serrano
Braz. J. Probab. Stat. 29(4): 767-777 (November 2015). DOI: 10.1214/14-BJPS245

Abstract

This paper revisits the Hölder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces $L^{p}(\mathcal{O})$, with $p\geq2$ 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 Brzeźniak (Stochastics Stochastics Rep. 61 (1997) 245–295).

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Rafael Serrano. "A note on space–time Hölder regularity of mild solutions to stochastic Cauchy problems in $L^{p}$-spaces." Braz. J. Probab. Stat. 29 (4) 767 - 777, November 2015. https://doi.org/10.1214/14-BJPS245

Information

Received: 1 July 2013; Accepted: 1 April 2014; Published: November 2015
First available in Project Euclid: 17 September 2015

zbMATH: 1334.60114
MathSciNet: MR3397392
Digital Object Identifier: 10.1214/14-BJPS245

Rights: Copyright © 2015 Brazilian Statistical Association

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Vol.29 • No. 4 • November 2015
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