caa a22 4500 605496994 CHVBK 20210128100539.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10543-014-0543-8 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0543-8 Multilevel Monte Carlo for the Feynman-Kac formula for the Laplace equation [Elektronische Daten] [Stefan Pauli, Robert Gantner, Peter Arbenz, Andreas Adelmann] 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. Springer Science+Business Media Dordrecht, 2015 Multilevel Monte Carlo nationallicence Feynman-Kac nationallicence Walk on Spheres nationallicence Laplace equation nationallicence Pauli Stefan Computer Science Department and Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland aut Gantner Robert Computer Science Department, ETH Zurich, Zurich, Switzerland aut Arbenz Peter Computer Science Department, ETH Zurich, Zurich, Switzerland aut Adelmann Andreas Large Research Facilities (GFA), Paul Scherrer Institute (PSI), Villigen, Switzerland aut BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 1125-1143 0006-3835 55:4<1125 2015 55 10543 https://doi.org/10.1007/s10543-014-0543-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0543-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pauli Stefan Computer Science Department and Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland aut NATIONALLICENCE 700 1- Gantner Robert Computer Science Department, ETH Zurich, Zurich, Switzerland aut NATIONALLICENCE 700 1- Arbenz Peter Computer Science Department, ETH Zurich, Zurich, Switzerland aut NATIONALLICENCE 700 1- Adelmann Andreas Large Research Facilities (GFA), Paul Scherrer Institute (PSI), Villigen, Switzerland aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 1125-1143 0006-3835 55:4<1125 2015 55 10543