The Annals of Applied Probability

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

Gonçalo dos Reis, William Salkeld, and Julian Tugaut

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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 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.

Article information

Source
Ann. Appl. Probab., Volume 29, Number 3 (2019), 1487-1540.

Dates
Received: August 2017
Revised: February 2018
First available in Project Euclid: 19 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1550566836

Digital Object Identifier
doi:10.1214/18-AAP1416

Mathematical Reviews number (MathSciNet)
MR3914550

Zentralblatt MATH identifier
07057460

Subjects
Primary: 60F10: Large deviations
Secondary: 60G07: General theory of processes

Keywords
McKean–Vlasov equations large deviations principle path-space Hölder topologies superlinear growth functional Strassen law

Citation

dos Reis, Gonçalo; Salkeld, William; Tugaut, Julian. Freidlin–Wentzell LDP in path space for McKean–Vlasov equations and the functional iterated logarithm law. Ann. Appl. Probab. 29 (2019), no. 3, 1487--1540. doi:10.1214/18-AAP1416. https://projecteuclid.org/euclid.aoap/1550566836


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