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**Harvard**

Andersson, A., Kovacs, M. och Larsson, S. (2016) *Weak error analysis for semilinear stochastic Volterra equations with additive noise*.

** BibTeX **

@article{

Andersson2016,

author={Andersson, Adam and Kovacs, Mihaly and Larsson, Stig},

title={Weak error analysis for semilinear stochastic Volterra equations with additive noise},

journal={Journal of Mathematical Analysis and Applications},

issn={0022-247X},

volume={437},

issue={2},

pages={1283-1304},

abstract={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.},

year={2016},

keywords={Stochastic Volterra equation; Finite element method; Backward Euler; Convolution quadrature; Strong and weak convergence; Malliavin calculus; Regularity; Duality},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 231523

A1 Andersson, Adam

A1 Kovacs, Mihaly

A1 Larsson, Stig

T1 Weak error analysis for semilinear stochastic Volterra equations with additive noise

YR 2016

JF Journal of Mathematical Analysis and Applications

SN 0022-247X

VO 437

IS 2

SP 1283

OP 1304

AB 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.

LA eng

DO 10.1016/j.jmaa.2015.09.016

LK http://dx.doi.org/10.1016/j.jmaa.2015.09.016

OL 30