Finite Kullback information diffusion laws with fixed marginals and associated large deviations functionals (Q1208948)

A theorem previously proved for the Wiener process on \(C([0,1],\mathbb{R}^ d)\) in [\textit{H. Föllmer}, Calcul de probabilités, Ec. d'Eté, Saint- Floor/Fr. 1985-87, Lect. Notes Math. 1362, 101-203 (1988; Zbl 0661.60063)] is extended to diffusion processes. Therefore, under slightly less general technical assumptions but in its whole generality, a theorem given by \textit{D. A. Dawson} and \textit{J. Gärtner} [Stochastics 20, 247- 308 (1987; Zbl 0613.60021)] is recovered. The result is intimately related with a Venttsel'-Frejdlin action functional associated to some \(N\)-particle system which is driven according to a nonlinear McKean- Vlasov limiting equation.