NDLI: Multilevel Monte Carlo method for parabolic stochastic partial differential equations

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Multilevel Monte Carlo method for parabolic stochastic partial differential equations

Content Provider	Springer Nature Link
Author	Lang, Annika Barth, Andrea Schwab, Christoph
Copyright Year	2012
Abstract	We analyze the convergence and complexity of multilevel Monte Carlo discretizations of a class of abstract stochastic, parabolic equations driven by square integrable martingales. We show under low regularity assumptions on the solution that the judicious combination of low order Galerkin discretizations in space and an Euler–Maruyama discretization in time yields mean square convergence of order one in space and of order 1/2 in time to the expected value of the mild solution. The complexity of the multilevel estimator is shown to scale log-linearly with respect to the corresponding work to generate a single path of the solution on the finest mesh, resp. of the corresponding deterministic parabolic problem on the finest mesh.
Ending Page	27
Page Count	25
Starting Page	3
File Format	PDF
ISSN	00063835
e-ISSN	15729125
Journal	BIT Numerical Mathematics
Issue Number	1
Volume Number	53
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-09-18
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stochastic partial differential equations Computational Mathematics and Numerical Analysis Numeric Computing Stochastic parabolic equation Mathematics Monte Carlo methods Multilevel Monte Carlo Stochastic differential and integral equations Multilevel approximations Computational methods for stochastic equations Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Stochastic Finite Element Methods Rate of convergence, degree of approximation
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

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