Weak error analysis for semilinear stochastic Volterra equations with additive noise
Artikel i vetenskaplig tidskrift, 2016

We prove a weak error estimate for the approximation in space and time of a semilinear stochastic Volterra integro-differential equation driven by additive space-time Gaussian noise. We treat this equation in an abstract framework, in which parabolic stochastic partial differential equations are also included as a special case. The approximation in space is performed by a standard finite element method and in time by an implicit Euler method combined with a convolution quadrature. The weak rate of convergence is proved to be twice the strong rate, as expected. Our convergence result concerns not only functionals of the solution at a fixed time but also more complicated functionals of the entire path and includes convergence of covariances and higher order statistics. The proof does not rely on a Kolmogorov equation. Instead it is based on a duality argument from Malliavin calculus.

Stochastic Volterra equation

Finite element method

Malliavin calculus

Convolution quadrature

Duality

Strong and weak convergence

Regularity

Backward Euler

Författare

Adam Andersson

Technische Universität Berlin

Mihaly Kovacs

University of Otago

Stig Larsson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Journal of Mathematical Analysis and Applications

0022-247X (ISSN) 1096-0813 (eISSN)

Vol. 437 1283-1304

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Fundament

Grundläggande vetenskaper

DOI

10.1016/j.jmaa.2015.09.016