Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schrödinger and linearized stochastic Korteweg-de Vries equations

Abstract

We establish weak convergence rates for noise discretizations of a wide class of stochastic evolution equations with non-regularizing semigroups and additive or multiplicative noise. This class covers the nonlinear stochastic wave, HJMM, stochastic Schrödinger and linearized stochastic Korteweg-de Vries equation. For several important equations, including the stochastic wave equation, previous methods give only suboptimal rates, whereas our rates are essentially sharp.

arXiv comment26 pages, minor revision

References in corpus (3)

• An exponential integrator scheme for time discretization of nonlinear stochastic wave equation
• Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces
• Numerical integration of Heath-Jarrow-Morton model of interest rates

Cited by in corpus (5)

• Weak convergence rates for an explicit full-discretization of stochastic Allen-Cahn equation with additive noise
• Weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise
• Numerical approximation and simulation of the stochastic wave equation on the sphere
• Temporal approximation of stochastic evolution equations with irregular nonlinearities
• Pathwise Uniform Convergence of Time Discretisation Schemes for SPDEs