Year: 2018
Type: article
Abstract: 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.
DOI: 10.1214/18-ecp150
Author: Daniel Lacker
Institution: Columbia University
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $675
OpenAlex ID: W2801910080