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Weak error analysis for semilinear stochastic Volterra equations with additive noise

Adam Andersson ; Mihaly Kovacs ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik)
Journal of Mathematical Analysis and Applications (0022-247X). Vol. 437 (2016), 2, p. 1283-1304.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Stochastic Volterra equation; Finite element method; Backward Euler; Convolution quadrature; Strong and weak convergence; Malliavin calculus; Regularity; Duality

Denna post skapades 2016-01-31. Senast ändrad 2016-03-16.
CPL Pubid: 231523


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Numerisk analys
Matematisk statistik

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