Multilevel Picard approximations for McKean-Vlasov stochastic differential equations

TL;DR

This paper introduces multilevel Picard approximation methods for McKean-Vlasov stochastic differential equations, significantly reducing computational effort and achieving near-optimal efficiency in high-dimensional settings.

Contribution

The authors develop full-history recursive multilevel Picard methods that improve computational efficiency for McKean-Vlasov equations, reducing effort from order 3 to nearly order 2+.

Findings

MLP approximations have computational effort of order 2+

Method is essentially optimal in high dimensions

Significant efficiency improvement over existing methods

Abstract

In the literatur there exist approximation methods for McKean-Vlasov stochastic differential equations which have a computational effort of order $3$. In this article we introduce full-history recursive multilevel Picard (MLP) approximations for McKean-Vlasov stochastic differential equations. We prove that these MLP approximations have computational effort of order $2+$ which is essentially optimal in high dimensions.