Large deviation principle for slow-fast systems with infinite-dimensional mixed fractional Brownian motion
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909784760909824 |
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| author | Xu, Wenting Xu, Yong Yang, Xiaoyu Pei, Bin |
| author_facet | Xu, Wenting Xu, Yong Yang, Xiaoyu Pei, Bin |
| contents | This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method which is based on the variational representation formula for infinite-dimensional mixed fractional Brownian motion. To obtain the weak convergence of the controlled systems, we apply the Khasminskii's averaging principle and the time discretization technique. In addition, we drop the boundedness assumption of the drift coefficients of the slow components and the diffusion coefficients of the fast components.Based on the proof of the large deviation principle, we also establish the moderate deviation principle for the slow-fast systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large deviation principle for slow-fast systems with infinite-dimensional mixed fractional Brownian motion Xu, Wenting Xu, Yong Yang, Xiaoyu Pei, Bin Probability 60F10, 60G15, 60H15 This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method which is based on the variational representation formula for infinite-dimensional mixed fractional Brownian motion. To obtain the weak convergence of the controlled systems, we apply the Khasminskii's averaging principle and the time discretization technique. In addition, we drop the boundedness assumption of the drift coefficients of the slow components and the diffusion coefficients of the fast components.Based on the proof of the large deviation principle, we also establish the moderate deviation principle for the slow-fast systems. |
| title | Large deviation principle for slow-fast systems with infinite-dimensional mixed fractional Brownian motion |
| topic | Probability 60F10, 60G15, 60H15 |
| url | https://arxiv.org/abs/2410.21785 |