Optimal Regularity for Semilinear Stochastic Partial Differential Equations with Multiplicative Noise

By Raphael Kruse, Stig Larsson. 2011

63 citations recorded by the source corpus.

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic parabolic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions and certain linear growth bounds. It is shown that the mild solution has the same optimal regularity properties as the stochastic convolution. The proof is elementary and makes use of existing results on the regularity of the solution, in particular, the Holder continuity with a non-optimal exponent.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/984586b0bbc832f210e1ee3c6762e97f3f5441f1

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Citations in the corpus

Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise (2014, unknown): “This is a new feature compared to the regularity analysis of [10, 17] for the memoryless case.”
A mild Itô formula for SPDEs (2010, background): “, Da Prato & Zabczyk [21, 22], Brzeźniak [8], Brzeźniak, Van Neerven, Veraar & Weis [9], Van Neerven, Veraar & Weis [102, 103, 104], Jentzen & Röckner [56], Kruse & Larsson [66] and the references therein), weak regularity for solutions of SPDEs seem to be much less investigated.”