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Weak error analysis for semilinear stochastic Volterra equations with additive noise

Adam Andersson (Institutionen för matematiska vetenskaper) ; Mihaly Kovacs ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik)

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.

Nyckelord: Stochastic Volterra equations, finite element method, backward Euler, convolution quadrature, strong and weak convergence, Malliavin calculus, regularity, duality

Denna post skapades 2014-11-25.
CPL Pubid: 206595


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)
Institutionen för matematiska vetenskaper, matematik (2005-2016)


Numerisk analys
Sannolikhetsteori och statistik

Chalmers infrastruktur

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On weak convergence, Malliavin calculus and Kolmogorov equations in infinite dimensions