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

Abstract

We show two Freidlin-Wentzell type Large Deviations Principles (LDP) in path space topologies (uniform and Hölder) for the solution process of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) using techniques which directly address the presence of the law in the coefficients and altogether avoiding decoupling arguments or limits of particle systems. We provide existence and uniqueness results along with several properties for a class of MV-SDEs having random coefficients and drifts of super-linear growth. As an application of our results, we establish a Functional Strassen type result (Law of Iterated Logarithm) for the solution process of a MV-SDE.

Final Version; 49 pages; To appear in Annals of Applied Probability

References in corpus (2)

• Large deviations and a Kramers' type law for self-stabilizing diffusions
• The enhanced Sanov theorem and propagation of chaos

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• Distribution dependent SDEs driven by additive continuous noise
• A flexible split-step scheme for solving McKean-Vlasov Stochastic Differential Equations
• Gamma Convergence Approach For The Large Deviations Of The Density In Systems Of Interacting Diffusion Processes