We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as e.g. exposed in Sznitmann . Our study was prompted by some concrete problems in battery modelling , and also by recent progrss on rough-pathwise McKean-Vlasov theory, notably Cass–Lyons , and then Bailleul, Catellier and Delarue . Such a “pathwise McKean-Vlasov theory” can be traced back to Tanaka . 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.
|Number of pages||31|
|Publication status||Published - 31 Dec 2018|