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arXiv · 2503.15906

The Onsager-Machlup functional for distribution dependent SDEs driven by fractional Brownian motion

Yanbin Zhu·Xiaomeng Jiang·Yong Li
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Abstract

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 H\"older norms of order $ \beta $ with $ 0 < \beta < H - \frac{1}{4} $. In the case $\frac{1}{2} < H < 1 $, the norms can be a H\"older norm of order $ \beta$ with $ H - \frac{1}{2} < \beta < H - \frac{1}{4} $. As an example, we compute the Onsager-Machlup functional for the stochastic pendulum equation

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Yanbin Zhu, Xiaomeng Jiang, Yong Li. 2025-03-20. The Onsager-Machlup functional for distribution dependent SDEs driven by fractional Brownian motion. https://arxiv.org/abs/2503.15906

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