Freidlin-Wentzell LDPs in path space for McKean-Vlasov equations and the Functional Iterated Logarithm Law

We show two Freidlin-Wentzell Large Deviations Principles for McKean-Vlasov Stochastic Differential Equations (MV-SDEs) in path space topologies using techniques addressing directly the presence of the law in the coefficients and avoiding altogether limits of particle systems. We work with MV-SDEs having a drift of polynomial growth and provide existence uniqueness results along with several properties.
As an application of our results, we establish a Functional Strassen type result (Law of Iterated Logarithm) for the solution of a MV-SDEs.