Weak error analysis for semilinear stochastic Volterra equations with additive noise

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

Stochastic Volterra equations

finite element method

backward Euler

convolution quadrature

strong and weak convergence

Malliavin calculus

regularity

duality

Publikations- och innehållstyp

vet (ämneskategori)

ovr (ämneskategori)