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

AbstractIn this article we extend a theorem previously proved by H. Föllmer for the Wiener process on C([0, 1], Rd) to diffusion processes; we therefore straightforward recover, under slightly less general technical assumptions but in its whole generality, a theorem already given by Dawson and Gärtner. The result is intimately related with a Ventcel-Freidlin action functional associated to some N-particle system which is driven according to a non-linear McKean-Vlasov limiting equation