## Importance sampling in path space for diffusion processes with slow-fast variables

• Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics. For certain exponential type expectation, the corresponding control force of the optimal change of measure leads to a zero-variance estimator and is related to the solution of a Hamilton–Jacobi–Bellmann equation. We focus on certain diffusions with both slow and fast variables, and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics. We demonstrate our approximation strategy with an illustrative numerical example.

Author: Carsten Hartmann, Christof Schütte, Marcus Weber, Wei Zhang Article Probability Theory and Related Fields 2017 If you are not subscribing to the journal please use the http link below as part of the Springer Nature SharedIt initiative http://rdcu.be/oA51 http://dx.doi.org/10.1007/s00440-017-0755-3
$Rev: 13581$