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Weak error analysis...
Weak error analysis for semilinear stochastic Volterra equations with additive noise
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- Andersson, Adam, 1979 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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Kovacs, Mihaly, 1977 (författare)
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- Larsson, Stig, 1952 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics
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(creator_code:org_t)
- 2014
- Engelska.
- Relaterad länk:
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https://gup.ub.gu.se...
Abstract
Ämnesord
Stäng
- 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)