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June 2019 Freidlin–Wentzell LDP in path space for McKean–Vlasov equations and the functional iterated logarithm law
Gonçalo dos Reis, William Salkeld, Julian Tugaut
Ann. Appl. Probab. 29(3): 1487-1540 (June 2019). DOI: 10.1214/18-AAP1416

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.

Citation

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Gonçalo dos Reis. William Salkeld. Julian Tugaut. "Freidlin–Wentzell LDP in path space for McKean–Vlasov equations and the functional iterated logarithm law." Ann. Appl. Probab. 29 (3) 1487 - 1540, June 2019. https://doi.org/10.1214/18-AAP1416

Information

Received: 1 August 2017; Revised: 1 February 2018; Published: June 2019
First available in Project Euclid: 19 February 2019

zbMATH: 07057460
MathSciNet: MR3914550
Digital Object Identifier: 10.1214/18-AAP1416

Subjects:
Primary: 60F10
Secondary: 60G07

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 3 • June 2019
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