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

2016/03/08 by Stüwe, Tobias, Barth, Andrea
#60H15 #65C30 #65M60 #65M70 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1603.02422

Abstract

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 approximation is derived. The convergence result is derived by use of the Malliavin derivative rather then the common approach via the Kolmogorov backward equation.

Related

• Malliavin regularity and weak approximation of semilinear SPDE with Lévy noise
• Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients
• Weak approximation of stochastic partial differential equations: the non linear case
• Weak convergence for a stochastic exponential integrator and finite element discretization of SPDE for multiplicative & additive noise
• Weak error estimates of Galerkin approximations for the stochastic Burgers equation driven by additive trace-class noise