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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.17766 |
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Table of Contents:
- In this manuscript, we investigate importance sampling methods for rare-event simulation in diffusion processes. We show, from a large-deviation perspective, that the resulting importance sampling estimator is log-efficient. This connection is established via a stochastic optimal control formulation, and the associated Hamilton--Jacobi--Bellman (HJB) equation is derived using dynamic programming. To approximate the optimal control, we adopt a spectral parameterization and employ the cross-entropy method to estimate the parameters by solving a least-squares problem. Finally, we present a numerical example to validate the effectiveness of the cross-entropy approach and the efficiency of the resulting importance sampling estimator.