Optimal Regularity for Semilinear Stochastic Partial Differential Equations with Multiplicative Noise

2011/09/29 by Raphael Kruse, Stig Larsson · 1 citation
Mathematics · #math.AP #math.PR #msc:35B65 #msc:35R60 #msc:60H15

paper · pdf · doi:10.1214/ejp.v17-2240

published as Electron. J. Probab. 17 (65) (2012), 1-19

arxiv created 2011/09/29 · arxiv updated 2012/08/21

Abstract

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions. 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 Hölder continuity with a non-optimal exponent.

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• Uniform-in-time weak error estimates of explicit full-discretization schemes for SPDEs with non-globally Lipschitz coefficients