Multilevel Picard approximations for McKean-Vlasov stochastic differential equations

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.

References in corpus (2)

• Full history recursive multilevel Picard approximations for ordinary differential equations with expectations
• Iterative Multilevel density estimation for McKean-Vlasov SDEs via projections

Cited by in corpus (2)

• A flexible split-step scheme for solving McKean-Vlasov Stochastic Differential Equations
• Strong $L^p$-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations