Open Access
2018 On a strong form of propagation of chaos for McKean-Vlasov equations
Daniel Lacker
Electron. Commun. Probab. 23: 1-11 (2018). DOI: 10.1214/18-ECP150


This note shows how to considerably strengthen the usual mode of convergence of an $n$-particle system to its McKean-Vlasov limit, often known as propagation of chaos, when the volatility coefficient is nondegenerate and involves no interaction term. Notably, the empirical measure converges in a much stronger topology than weak convergence, and any fixed $k$ particles converge in total variation to their limit law as $n\rightarrow \infty $. This requires minimal continuity for the drift in both the space and measure variables. The proofs are purely probabilistic and rather short, relying on Girsanov’s and Sanov’s theorems. Along the way, some modest new existence and uniqueness results for McKean-Vlasov equations are derived.


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Daniel Lacker. "On a strong form of propagation of chaos for McKean-Vlasov equations." Electron. Commun. Probab. 23 1 - 11, 2018.


Received: 11 May 2018; Accepted: 8 July 2018; Published: 2018
First available in Project Euclid: 27 July 2018

zbMATH: 1396.65013
MathSciNet: MR3841406
Digital Object Identifier: 10.1214/18-ECP150

Primary: 35K59 , 60K35 , 65C35

Keywords: Burgers equation , McKean-Vlasov equation , Particle system , propagation of chaos

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