Multilevel Monte Carlo method for parabolic stochastic partial differential equations
Open access
Datum
2011-05Typ
- Report
ETH Bibliographie
yes
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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. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-a-010402968Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
SAM Research ReportBand
Verlag
Seminar for Applied Mathematics, ETH ZurichAusgabe / Version
Revised: August 2012Organisationseinheit
03435 - Schwab, Christoph / Schwab, Christoph
Förderung
247277 - Automated Urban Parking and Driving (EC)
Zugehörige Publikationen und Daten
Is previous version of: https://doi.org/10.3929/ethz-b-000059248
ETH Bibliographie
yes
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