Heavy tailed large deviations for time averages of diffusions: the Ornstein-Uhlenbeck case
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911064857247744 |
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| author | Ferré, Grégoire |
| author_facet | Ferré, Grégoire |
| contents | We study large deviations for the time average of the Ornstein-Uhlenbeck process raised to an arbitrary power. We prove that beyond a critical value, large deviations are subexponential in time, with a non-convex rate function whose main coefficient is given by the solution to a Hamilton-Jacobi problem. Although a similar problem was addressed in a recent work, the originality of the paper is to provide a short, self-contained proof of this result through a couple of standard large deviations arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16992 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heavy tailed large deviations for time averages of diffusions: the Ornstein-Uhlenbeck case Ferré, Grégoire Probability Statistical Mechanics We study large deviations for the time average of the Ornstein-Uhlenbeck process raised to an arbitrary power. We prove that beyond a critical value, large deviations are subexponential in time, with a non-convex rate function whose main coefficient is given by the solution to a Hamilton-Jacobi problem. Although a similar problem was addressed in a recent work, the originality of the paper is to provide a short, self-contained proof of this result through a couple of standard large deviations arguments. |
| title | Heavy tailed large deviations for time averages of diffusions: the Ornstein-Uhlenbeck case |
| topic | Probability Statistical Mechanics |
| url | https://arxiv.org/abs/2402.16992 |