Freidlin-Wentzell type exit-time estimates for time-inhomogeneous diffusions and their applications
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912196971200512 |
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| author | Aleksian, Ashot Villeneuve, Stéphane |
| author_facet | Aleksian, Ashot Villeneuve, Stéphane |
| contents | This paper investigates the exit-time problem for time-inhomogeneous diffusion processes. The focus is on the small-noise behavior of the exit time from a bounded positively invariant domain. We demonstrate that, when the drift and diffusion terms are uniformly close to some time-independent functions, the exit time grows exponentially both in probability and in $L_1$ as a parameter that controls the noise tends to zero. We also characterize the exit position of the time-inhomogeneous process. Additionally, we investigate the impact of relaxing the uniform closeness condition on the exit-time behavior. As an application, we extend these results to the McKean-Vlasov process. Our findings improve upon existing results in the literature for the exit-time problem for this class of processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Freidlin-Wentzell type exit-time estimates for time-inhomogeneous diffusions and their applications Aleksian, Ashot Villeneuve, Stéphane Probability 60H10, 60J60, 60K35 This paper investigates the exit-time problem for time-inhomogeneous diffusion processes. The focus is on the small-noise behavior of the exit time from a bounded positively invariant domain. We demonstrate that, when the drift and diffusion terms are uniformly close to some time-independent functions, the exit time grows exponentially both in probability and in $L_1$ as a parameter that controls the noise tends to zero. We also characterize the exit position of the time-inhomogeneous process. Additionally, we investigate the impact of relaxing the uniform closeness condition on the exit-time behavior. As an application, we extend these results to the McKean-Vlasov process. Our findings improve upon existing results in the literature for the exit-time problem for this class of processes. |
| title | Freidlin-Wentzell type exit-time estimates for time-inhomogeneous diffusions and their applications |
| topic | Probability 60H10, 60J60, 60K35 |
| url | https://arxiv.org/abs/2501.11797 |