PATHWISE MCKEAN-VLASOV THEORY WITH ADDITIVE NOISE

• 成果类型: Article
• 署名作者: Coghi, Michele; Deuschel, Jean-Dominique; Friz, Peter K.; Maurelli, Mario
• 署名单位: Technical University of Berlin; Technical University of Berlin; University of Milan
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1560
• 发表日期: 2020
• 页码: 2355-2392
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; mean-field games; interacting particles; propagation; chaos; DIFFUSIONS; domain; limit

摘要

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.