Weak convergence of Galerkin approximations of stochastic partial differential equations driven by additive Lévy noise

This work considers weak approximations of stochastic partial differential equations (SPDEs) driven by Lévy noise. The SPDEs at hand are parabolic with additive noise processes. A weak-convergence rate for the corresponding Galerkin Finite Element approximation is derived. The convergence result is derived by use of the Malliavin derivative rather than the common approach via the Kolmogorov backward equation.