$L^p$-valued stochastic convolution integral driven by Volterra noise

Petr Čoupek; Bohdan Maslowski; Martin Ondreját

doi:10.1142/s021949371850048x

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arXiv · 1704.03307

$L^p$-valued stochastic convolution integral driven by Volterra noise

Petr Čoupek·Bohdan Maslowski·Martin Ondreját

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Abstract

Space-time regularity of linear stochastic partial differential equations is studied. The solution is defined in the mild sense in the state space $L^p$. The corresponding regularity is obtained by showing that the stochastic convolution integrals are H\"{o}lder continuous in a suitable function space. In particular cases, this allows to show space-time H\"{o}lder continuity of the solution. The main tool used is a hypercontractivity result on Banach-space valued random variables in a finite Wiener chaos.

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Petr Čoupek, Bohdan Maslowski, Martin Ondreját. 2017-04-11. $L^p$-valued stochastic convolution integral driven by Volterra noise. https://doi.org/10.1142/s021949371850048x

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