# Pathwise McKean-Vlasov Theory with Additive Noise

## TL;DR

This paper develops a pathwise approach to McKean-Vlasov stochastic differential equations with additive noise, enabling new applications and generalizations beyond traditional probabilistic methods.

## Contribution

It introduces a simplified, versatile pathwise framework for McKean-Vlasov equations, extending to non-Brownian noise, reflecting boundaries, and mean field convergence without independence assumptions.

## Key findings

- Mean field convergence without a priori independence
- Extension of large deviations and CLT to non-Brownian noise
- Application to battery modeling and rough-path theory

## 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, c\`adl\`ag noise, and reflecting boundaries. Last not least, we generalize Dawson-G\"artner large deviations and the central limit theorem to a non-Brownian noise setting.