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

Abstract

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 sam- pling 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 diffu- sions 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.

41 pages

References in corpus (3)

• Efficient rare-event simulation for the maximum of heavy-tailed random walks
• Effective interactions and large deviations in stochastic processes
• Large Deviations and Importance Sampling for Systems of Slow-Fast Motion

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