The Onsager-Machlup functional for distribution dependent SDEs driven by fractional Brownian motion
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910886061408256 |
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| author | Zhu, Yanbin Jiang, Xiaomeng Li, Yong |
| author_facet | Zhu, Yanbin Jiang, Xiaomeng Li, Yong |
| contents | In this paper, we compute the Onsager-Machlup functional for distribution dependent SDEs driven by fractional Brownian motions with Hurst
parameter $H\in (\frac{1}{4},1)$. In the case $ \frac{1}{4} < H < \frac{1}{2} $, the norm can be either the supremum norm or Hölder norms of order $ β$ with $ 0 < β< H - \frac{1}{4} $. In the case $\frac{1}{2} < H < 1 $, the norms can be a Hölder norm of order $ β$ with $ H - \frac{1}{2} < β< H - \frac{1}{4} $. As an example, we compute the Onsager-Machlup functional for the stochastic pendulum equation |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_15906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Onsager-Machlup functional for distribution dependent SDEs driven by fractional Brownian motion Zhu, Yanbin Jiang, Xiaomeng Li, Yong Dynamical Systems Probability 60H10, 60G22, 82C35 In this paper, we compute the Onsager-Machlup functional for distribution dependent SDEs driven by fractional Brownian motions with Hurst parameter $H\in (\frac{1}{4},1)$. In the case $ \frac{1}{4} < H < \frac{1}{2} $, the norm can be either the supremum norm or Hölder norms of order $ β$ with $ 0 < β< H - \frac{1}{4} $. In the case $\frac{1}{2} < H < 1 $, the norms can be a Hölder norm of order $ β$ with $ H - \frac{1}{2} < β< H - \frac{1}{4} $. As an example, we compute the Onsager-Machlup functional for the stochastic pendulum equation |
| title | The Onsager-Machlup functional for distribution dependent SDEs driven by fractional Brownian motion |
| topic | Dynamical Systems Probability 60H10, 60G22, 82C35 |
| url | https://arxiv.org/abs/2503.15906 |