Open access
Date
2015-12Type
- Journal Article
ETH Bibliography
yes
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Abstract
Since its formulation in the late 1940s, the Feynman–Kac formula has proven to be an effective tool for both theoretical reformulations and practical simulations of differential equations. The link it establishes between such equations and stochastic processes can be exploited to develop Monte Carlo sampling methods that are effective, especially in high dimensions. There exist many techniques of improving standard Monte Carlo sampling methods, a relatively new development being the so-called Multilevel Monte Carlo method. This paper investigates the applicability of multilevel ideas to the stochastic representation of partial differential equations by the Feynman–Kac formula, using the Walk on Spheres algorithm to generate the required random paths. We focus on the Laplace equation, the simplest elliptic PDE, while mentioning some extension possibilities. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000107181Publication status
publishedExternal links
Journal / series
BIT Numerical MathematicsVolume
Pages / Article No.
Publisher
SpringerSubject
Multilevel Monte Carlo; Feynman–Kac; Walk on Spheres; Laplace equation; 60H30; 65C05; 65N99Organisational unit
08805 - Arbenz, Peter (Tit.-Prof.)
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.More
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ETH Bibliography
yes
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