A Short Report on Importance Sampling for Rare Event Simulation in Diffusions

Zhiwei Gao

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arXiv · 2512.17766

A Short Report on Importance Sampling for Rare Event Simulation in Diffusions

Zhiwei Gao

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Abstract

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.

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Zhiwei Gao. 2025-12-19. A Short Report on Importance Sampling for Rare Event Simulation in Diffusions. https://arxiv.org/abs/2512.17766

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