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

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