Weak convergence of Galerkin approximations of stochastic partial differential equations driven by additive L\'evy noise

TL;DR

This paper establishes a weak convergence rate for Galerkin approximations of parabolic SPDEs driven by Le9vy noise, using Malliavin calculus instead of traditional methods, advancing numerical analysis of stochastic PDEs.

Contribution

It introduces a novel approach employing Malliavin derivatives to analyze weak convergence of Galerkin methods for SPDEs with Le9vy noise, differing from classical techniques.

Findings

Derived weak convergence rate for Galerkin approximations

Used Malliavin calculus instead of Kolmogorov backward equation

Applicable to parabolic SPDEs with additive Le9vy noise

Abstract

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