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 $\Vert \cdot {\Vert }_{\infty }$, H$\ddot{\mathrm{o}}$lder norms $\Vert \cdot {\Vert }_{\alpha }$ 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.

References in corpus (1)

• Stochastic analysis in a tubular neighborhood or Onsager-Machlup functions revisited