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

By Gonçalo dos Reis, William Salkeld, Julian Tugaut. The Annals of Applied Probability, 2017

128 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/a77b5de24e82755d693e058a941819a6c076465a

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1. Jianliang Zhai
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1. Jianliang Zhai
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Citations in the corpus

• Large and Moderate Deviation Principles for McKean-Vlasov SDEs with Jumps (2020, background): “Thus, our assumptions are clearly weaker than those of [20].”
• McKean–Vlasov SDEs under measure dependent Lyapunov conditions (2018, unknown): “g [6, 15, 26, 37].”