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August  2019, 24(8): 4271-4294. doi: 10.3934/dcdsb.2019081

## Malliavin regularity and weak approximation of semilinear SPDEs with Lévy noise

 1 Smarter AI Sweden, Vallgatan 3, SE-411-16 Gothenburg, Sweden 2 Institute of Mathematics, University of Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany

* Corresponding author: Felix Lindner

Received  June 2018 Revised  November 2018 Published  August 2019 Early access  April 2019

We investigate the weak order of convergence for space-time discrete approximations of semilinear parabolic stochastic evolution equations driven by additive square-integrable Lévy noise. To this end, the Malliavin regularity of the solution is analyzed and recent results on refined Malliavin-Sobolev spaces from the Gaussian setting are extended to a Poissonian setting. For a class of path-dependent test functions, we obtain that the weak rate of convergence is twice the strong rate.

Citation: Adam Andersson, Felix Lindner. Malliavin regularity and weak approximation of semilinear SPDEs with Lévy noise. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4271-4294. doi: 10.3934/dcdsb.2019081
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