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Malliavin regularity and weak approximation of semilinear SPDEs with Lévy noise

  • * Corresponding author: Felix Lindner

    * Corresponding author: Felix Lindner
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  • 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.

    Mathematics Subject Classification: Primary: 60H15, 60G51, 60H07; Secondary: 65C30, 65M60.


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