The Onsager-Machlup action functional for degenerate McKean-Vlasov Stochastic Differential Equations

Abstract: The purpose of this paper is to investigate the existence of the Onsager-Machlup action functional for degenerate McKean-Vlasov stochastic differential equations. To this end, we first derive Onsager-Machlup action functional for degenerate McKean-Vlasov stochastic differential equations with constant diffusion in a broad set of norms by Girsanov transformation, some conditioned exponential inequalities and It$\mathrm{\hat{o}}$ formulas for distribution dependent functional. Then an example is given to illustrate our results.