OS Partielle Differentialgleichungen: Pathwise McKean-Vlasov Theory
Wann
Mittwoch, 6. Februar 2019
13:30 bis 15 Uhr
Wo
D 435
Veranstaltet von
Vortragende Person/Vortragende Personen:
Dr. Luigi Coghi (WIAS Berlin)
Diese Veranstaltung ist Teil der Veranstaltungsreihe „Oberseminar Partielle Differentialgleichungen“.
Zusammenfassung: We take a pathwise approach to classical McKean-Vlasov stochastic di fferential equations with additive noise, as e.g. exposed in [Sznitmann, 1991]. Our study was prompted by some concrete problems in battery modelling as presented in [Guhlke et al., 2018], and also by recent progress on rough-pathwise McKean-Vlasov theory, notably [Cass, Lyons 2014], and then [Bailleul et al. 2018]. Such a "pathwise McKean-Vlasov theory" can be traced back to [Tanaka, 1982]. This can be seen as an attempt to advertise the ideas, power and simplicity of the pathwise approach, not so easily extracted from the recent rough-paths works. As novel applications we discuss mean field convergence without a priori independence and exchangeability assumption; common noise and reflecting boundaries. Last but not least, we generalise Dawson-Gartner large deviations to a non-Brownian noise setting.