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Author
Date
2010-06Type
- Report
ETH Bibliography
yes
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Abstract
The numerical discretization of problems with stochastic data or stochastic parameters generally involves the introduction of coordinates that describe the stochastic behavior, such as coefficients in a series expansion or values at discrete points. The series expansion of a Gaussian field with respect to any orthonormal basis of its Cameron--Martin space has independent standard normal coefficients. A standard choice for numerical simulations is the Karhunen-Loève series, which is based on eigenfunctions of the covariance operator. We suggest an alternative basis that can be constructed directly from the covariance kernel. The resulting basis functions are often well localized, and the convergence of the series expansion seems to be comparable to that of the Karhunen--Lo\`eve series. We provide explicit formulas for particular cases, and general numerical methods for computing exact representations of such bases. Finally, we relate our approach to numerical discretizations based on replacing a random field by its values on a finite set. Show more
Permanent link
https://doi.org/10.3929/ethz-a-010403532Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichOrganisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
Funding
247277 - Automated Urban Parking and Driving (EC)
Related publications and datasets
Is previous version of: https://doi.org/10.3929/ethz-b-000159419
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ETH Bibliography
yes
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