Physics

Control engineering

Decoupling (probability)

Uniqueness

Mathematics

Strassen algorithm

Logarithm

Stochastic differential equation

Statistics

Iterated logarithm

Engineering

Mathematical analysis

Law of the iterated logarithm

Matrix multiplication

Rate function

Quantum mechanics

Applied mathematics

Large deviations theory

Quantum

The Annals of Applied Probability

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 superlinear 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.

Freidlin–Wentzell LDP in path space for McKean–Vlasov equations and the functional iterated logarithm law