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

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 Hölder continuous in a suitable function space. In particular cases, this allows to show space-time Hölder continuity of the solution. The main tool used is a hypercontractivity result on Banach-space valued random variables in a finite Wiener chaos.

Accepted manuscript

References in corpus (1)

• Analysis of the Rosenblatt process

Cited by in corpus (4)

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