A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes

DOI10.1007/978-3-319-33507-0_25zbMath1356.65020arXiv1508.07958OpenAlexW2153731280MaRDI QIDQ2957052

Annika Lang

Publication date: 20 January 2017

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.07958

zbMATH Keywords

computational complexityweak convergencestochastic partial differential equationsstochastic heat equationfinite element approximationsmultilevel Monte Carlo methodsweak error analysisnumerical exampes

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Complexity and performance of numerical algorithms (65Y20)

Related Items (6)

Numerical analysis of lognormal diffusions on the sphere ⋮ A Fully Parallelizable Space-Time Multilevel Monte Carlo Method for Stochastic Differential Equations with Additive Noise ⋮ Combining Space-Time Multigrid Techniques with Multilevel Monte Carlo Methods for SDEs ⋮ Rapid Covariance-Based Sampling of Linear SPDE Approximations in the Multilevel Monte Carlo Method ⋮ Monte Carlo versus multilevel Monte Carlo in weak error simulations of SPDE approximations ⋮ Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs

Cites Work

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• Duality in refined Sobolev-Malliavin spaces and weak approximation of SPDE
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• \(L^p\) and almost sure convergence of a Milstein scheme for stochastic partial differential equations
• Multilevel Monte Carlo Path Simulation
• Simulation of stochastic partial differential equations using finite element methods
• Multilevel Monte Carlo method with applications to stochastic partial differential equations

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