SDE based regression for random PDEs

A simulation based method for the numerical solution of PDE with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to an approximation of the global solution of the random PDE. We provide an initial error and complexity analysis of the proposed method along with numerical examples illustrating its behaviour.

Keywords

Partial differential equations with random coefficients, random PDE, uncertainty quantification, Feynman-Kac, stochastic differential equations, stochastic simulation, stochastic regression, Monte-Carlo, Euler-Maruyama

URI

https://doi.org/10.34657/3124
https://oa.tib.eu/renate/handle/123456789/3505

Citation

Anker, F., Bayer, C., Eigel, M., Ladkau, M., Neumann, J., & Schoenmakers, J. G. M. (2015). SDE based regression for random PDEs (Vol. 2192). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.

Collections

Mathematik

License

Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.

Full item page