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

TL;DR

This paper establishes large deviations principles and a Law of Iterated Logarithm for solutions of McKean-Vlasov SDEs, advancing understanding of their path space behavior without relying on particle system limits.

Contribution

It introduces direct techniques for LDP in path space for MV-SDEs, avoiding decoupling and particle system limits, and proves a Functional Strassen Law for these equations.

Findings

Proved LDP in uniform and Hölder topologies for MV-SDE solutions.

Established existence and uniqueness for MV-SDEs with random coefficients and super-linear drifts.

Derived a Law of Iterated Logarithm for MV-SDE solutions.

Abstract

We show two Freidlin-Wentzell type Large Deviations Principles (LDP) in path space topologies (uniform and H\"older) 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.