Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.17766 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909971162071040 |
|---|---|
| author | Gao, Zhiwei |
| author_facet | Gao, Zhiwei |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Short Report on Importance Sampling for Rare Event Simulation in Diffusions Gao, Zhiwei Numerical Analysis Probability 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. |
| title | A Short Report on Importance Sampling for Rare Event Simulation in Diffusions |
| topic | Numerical Analysis Probability |
| url | https://arxiv.org/abs/2512.17766 |