Pathwise McKean-Vlasov Theory with Additive Noise
arXiv:1812.11773 · doi:10.1214/20-AAP1560
Abstract
Abstract. We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as e.g. exposed in Sznitmann [38]. Our study was prompted by some concrete problems in battery modelling [23], and also by recent progrss on rough-pathwise McKean-Vlasov theory, notably Cass-Lyons [10], and then Bailleul, Catellier and Delarue [4]. Such a "pathwise McKean-Vlasov theory" can be traced back to Tanaka [40]. 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, 10, 40], 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.
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- Distribution dependent SDEs driven by additive continuous noise
- Rough nonlocal diffusions
- A stochastic PDE approach to large N problems in quantum field theory: a survey
- Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering
- Solving McKean-Vlasov SDEs via relative entropy
- Small ball probabilities, metric entropy and Gaussian rough paths
- Rough path theory