The Onsager-Machlup action functional for Mckean-Vlasov SDEs

Abstract: This paper is devoted to deriving the Onsager-Machlup action functional for Mckean-Vlasov stochastic differential equations in a class of norms that dominate $L^2([0,1], \mathbb{R}^d)$, such as supremum norm $|\cdot|{\infty}$, H$\mathrm{\ddot{o}}$lder norms $|\cdot|{\alpha}$ with $\alpha<\frac{1}{4}$ and $L^p$-norms with $p>4$ are included. Moreover, the corresponding Euler-Lagrange equation for Onsager-Machlup action functional is derived and a example is given.