Milstein approximation for advection-diffusion equations driven by multiplicative noncontinuous martingale noises
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Date
2011-05Type
- Report
ETH Bibliography
yes
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Abstract
In this paper the strong approximation of a stochastic partial differential equation, whose differential operator is of advection--diffusion type and which is driven by a multiplicative infinite-dimensional càdlàg square integrable martingale, is presented. A finite-dimensional projection of the infinite-dimensional equation, for example a Galerkin projection, with adapted time stepping is used. Error estimates for the discretized equation are derived in $L^2$ and almost sure senses. Besides space and time discretizations, noise approximations are also provided. Finally, simulations complete the paper. Show more
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Finite Element method; Stochastic partial differential equation; Martingale; Galerkin method; Zakai equation; Advection-diffusion PDE; Milstein scheme; Crank--Nicolson approximation; Karhunen-Loève expansion; Adapted time steppingOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
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Is previous version of: https://doi.org/10.3929/ethz-a-010400810
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