Malliavin regularity and weak approximation of semilinear SPDE with L\'evy noise

Adam Andersson; Felix Lindner

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arXiv · 1808.08574

Malliavin regularity and weak approximation of semilinear SPDE with L\'evy noise

Adam Andersson·Felix Lindner

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Abstract

We investigate the weak order of convergence for space-time discrete approximations of semilinear parabolic stochastic evolution equations driven by additive square-integrable L\'evy 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.

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Adam Andersson, Felix Lindner. 2018-08-26. Malliavin regularity and weak approximation of semilinear SPDE with L\'evy noise. https://arxiv.org/abs/1808.08574

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