Averaging principle for slow-fast fractional stochastic differential equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911192247697408 |
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| author | Bréhier, Charles-Edouard Faye, Ibrahima |
| author_facet | Bréhier, Charles-Edouard Faye, Ibrahima |
| contents | We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component considered as solution to an ergodic stochastic differential equation driven by a standard Brownian motion. We establish the convergence of the slow component when the time-scale separation vanishes to the solution of the so-called averaged equation, which is an autonomous fractional differential equation, in the mean-square sense. Moreover, when the fast component does not depend on the slow component, we provide a rate of convergence depending on the order of the fractional derivative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04129 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Averaging principle for slow-fast fractional stochastic differential equations Bréhier, Charles-Edouard Faye, Ibrahima Probability We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component considered as solution to an ergodic stochastic differential equation driven by a standard Brownian motion. We establish the convergence of the slow component when the time-scale separation vanishes to the solution of the so-called averaged equation, which is an autonomous fractional differential equation, in the mean-square sense. Moreover, when the fast component does not depend on the slow component, we provide a rate of convergence depending on the order of the fractional derivative. |
| title | Averaging principle for slow-fast fractional stochastic differential equations |
| topic | Probability |
| url | https://arxiv.org/abs/2510.04129 |