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.
Pathwise McKean–Vlasov theory with additive noise / M. Coghi, J. Deuschel, P.K. Friz, M. Maurelli. - In: THE ANNALS OF APPLIED PROBABILITY. - ISSN 1050-5164. - 30:5(2020), pp. 2355-2392.
|Titolo:||Pathwise McKean–Vlasov theory with additive noise|
|Parole Chiave:||Mean field; McKean-Vlasov; large deviations; central limit theorem; jump-processes; additive noise|
|Settore Scientifico Disciplinare:||Settore MAT/06 - Probabilita' e Statistica Matematica|
|Data di pubblicazione:||2020|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1214/20-AAP1560|
|Appare nelle tipologie:||01 - Articolo su periodico|