Rare event simulation via importance sampling for linear SPDE's
Files
Accepted manuscript
Date
2017-05-22
DOI
Authors
Salins, Michael
Spiliopoulos, Konstantinos
Version
Accepted manuscript
OA Version
Citation
Michael Salins, Konstantinos Spiliopoulos. 2017. "Rare event simulation via importance sampling for linear SPDE's." Stochastics and Partial Differential Equations: Analysis and Computations, Volume 5, Issue 4, pp. 652 - 690 (38).
Abstract
The goal of this paper is to develop provably efficient importance sampling Monte Carlo methods for the estimation of rare events within the class of linear stochastic partial differential equations (SPDEs). We find that if a spectral gap of appropriate size exists, then one can identify a lower dimensional manifold where the rare event takes place. This allows one to build importance sampling changes of measures that perform provably well even pre-asymptotically (i.e. for small but non-zero size of the noise) without degrading in performance due to infinite dimensionality or due to long simulation time horizons. Simulation studies supplement and illustrate the theoretical results.