Pathwise McKean-Vlasov Theory

Michele Coghi, Jean-Dominique Deuschel, Peter K. Friz, Mario Maurelli

Research output: Working paper


We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as e.g. exposed in Sznitmann [33]. Our study was prompted by some concrete problems in battery modelling [17], and also by recent progrss on rough-pathwise McKean-Vlasov theory, notably Cass–Lyons [7], and then Bailleul, Catellier and Delarue [4]. Such a “pathwise McKean-Vlasov theory” can be traced back to Tanaka [35]. This paper can be seen as an attempt to advertize the ideas, power and simplicity of the pathwise appproach, not so easily extracted from [4,7,35]. As novel applications we discuss mean field convergence without a priori independence and exchangeability assumption; common noise and reflecting boundaries. Last not least, we generalize Dawson–G¨artner large deviations to a non-Brownian noise setting.
Original languageEnglish
Number of pages31
Publication statusPublished - 31 Dec 2018


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