Pathwise Mckean-Vlasov Theory With Additive Noise

We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as for example, exposed in Sznitmann (In Ecole D Ete de Probabilites de Saint-Flour XIX-1989 (1991) 165-251, Springer). Our study was prompted by some concrete problems in battery modelling (Contin. Mech. Thennodyn. 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, cadlag noise, and reflecting boundaries. Last not least, we generalize Dawson-Gartner large deviations and the central limit theorem to a non-Brownian noise setting.