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October 2020 Pathwise McKean–Vlasov theory with additive noise
Michele Coghi, Jean-Dominique Deuschel, Peter K. Friz, Mario Maurelli
Ann. Appl. Probab. 30(5): 2355-2392 (October 2020). DOI: 10.1214/20-AAP1560

Abstract

We take a pathwise approach to classical McKean–Vlasov stochastic differential equations with additive noise, as for example, exposed in Sznitmann (In École D’Été de Probabilités de Saint-Flour XIX—1989 (1991) 165–251, Springer). Our study was prompted by some concrete problems in battery modelling (Contin. Mech. Thermodyn. 30 (2018) 593–628), and also by recent progrss on rough-pathwise McKean–Vlasov theory, notably Cass–Lyons (Proc. Lond. Math. Soc. (3) 110 (2015) 83–107), and then Bailleul, Catellier and Delarue (Bailleul, Catellier and Delarue (2018)). Such a “pathwise McKean–Vlasov theory” can be traced back to Tanaka (In Stochastic Analysis (Katata/Kyoto, 1982) (1984) 469–488, North-Holland). This paper can be seen as an attempt to advertize the ideas, power and simplicity of the pathwise appproach, not so easily extracted from (Bailleul, Catellier and Delarue (2018); Proc. Lond. Math. Soc. (3) 110 (2015) 83–107; In Stochastic Analysis (Katata/Kyoto, 1982) (1984) 469–488, North-Holland), together with a number of novel applications. These include mean field convergence without a priori independence and exchangeability assumption; common noise, càdlàg noise, and reflecting boundaries. Last not least, we generalize Dawson–Gärtner large deviations and the central limit theorem to a non-Brownian noise setting.

Citation

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Michele Coghi. Jean-Dominique Deuschel. Peter K. Friz. Mario Maurelli. "Pathwise McKean–Vlasov theory with additive noise." Ann. Appl. Probab. 30 (5) 2355 - 2392, October 2020. https://doi.org/10.1214/20-AAP1560

Information

Received: 1 December 2018; Revised: 1 September 2019; Published: October 2020
First available in Project Euclid: 15 September 2020

MathSciNet: MR4149531
Digital Object Identifier: 10.1214/20-AAP1560

Subjects:
Primary: 60F05, 60F10, 60F15, 60G09, 60H10, 60J50

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 5 • October 2020
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