TY - UNPB

T1 - Pathwise McKean-Vlasov Theory

AU - Coghi, Michele

AU - Deuschel, Jean-Dominique

AU - Friz, Peter K.

AU - Maurelli, Mario

PY - 2018/12/31

Y1 - 2018/12/31

N2 - 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.

AB - 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.

M3 - Working paper

BT - Pathwise McKean-Vlasov Theory

PB - ArXiv

ER -