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Duality in refined ...
Duality in refined Sobolev–Malliavin spaces and weak approximation of SPDE
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- Andersson, Adam, 1979 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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Kruse, Raphael, 1983 (författare)
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- Larsson, Stig, 1952 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- 2015-10-27
- 2016
- Engelska.
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Ingår i: Stochastic Partial Differential Equations: Analysis and Computations. - : Springer Science and Business Media LLC. - 2194-0401 .- 2194-041X. ; 4:1, s. 113-149
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Abstract
Ämnesord
Stäng
- We introduce a new family of refined Sobolev–Malliavin spaces that capture the integrability in time of the Malliavin derivative. We consider duality in these spaces and derive a Burkholder type inequality in a dual norm. The theory we develop allows us to prove weak convergence with essentially optimal rate for numerical approximations in space and time of semilinear parabolic stochastic evolution equations driven by Gaussian additive noise. In particular, we combine a standard Galerkin finite element method with backward Euler timestepping. The method of proof does not rely on the use of the Kolmogorov equation or the Itō formula and is therefore non-Markovian in nature. Test functions satisfying polynomial growth and mild smoothness assumptions are allowed, meaning in particular that we prove convergence of arbitrary moments with essentially optimal rate.
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
- SPDE
- Finite element method
- Backward Euler
- Weak convergence
- Convergence of moments
- Malliavin calculus
- Duality
- Spatio-temporal discretization
- Malliavin calculus
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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