Importance Sampling for Multiscale Diffusions
Probability
2012-02-03 v1 Systems and Control
Optimization and Control
Abstract
We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale processes there are additional complications, and indeed the straightforward adaptation of methods for standard small noise diffusions will not produce efficient schemes. Using the subsolution approach we construct schemes and identify conditions under which the schemes will be asymptotically optimal. Examples and simulation results are provided.
Cite
@article{arxiv.1107.5448,
title = {Importance Sampling for Multiscale Diffusions},
author = {Paul Dupuis and Konstantinos Spiliopoulos and Hui Wang},
journal= {arXiv preprint arXiv:1107.5448},
year = {2012}
}