Multilevel Monte Carlo method for parabolic stochastic partial differential equations
Open access
Date
2011-05Type
- Report
ETH Bibliography
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. Show more
Permanent link
https://doi.org/10.3929/ethz-a-010402968Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichEdition / version
Revised: August 2012Organisational unit
03435 - Schwab, Christoph / Schwab, Christoph
Funding
247277 - Automated Urban Parking and Driving (EC)
Related publications and datasets
Is previous version of: https://doi.org/10.3929/ethz-b-000059248
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ETH Bibliography
yes
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