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 Hölder norms of order $\beta$ with $0<\beta <H-\frac{1}{4}$. In the case $\frac{1}{2}<H<1$, the norms can be a Hölder 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