Weak error analysis for semilinear stochastic Volterra equations with additive noise
Preprint, 2014

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 weak convergence result concerns not only the solution at a fixed time but also integrals of the entire path with respect to any finite Borel measure. The proof does not rely on a Kolmogorov equation. Instead it is based on a duality argument from Malliavin calculus.

backward Euler

strong and weak convergence

Malliavin calculus

Stochastic Volterra equations

regularity

convolution quadrature

duality

finite element method

Författare

Adam Andersson

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Stig Larsson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Fundament

Grundläggande vetenskaper