On modified Euler methods for McKean-Vlasov stochastic differential equations with super-linear coefficients

TL;DR

This paper develops and analyzes a new class of modified Euler methods for solving McKean-Vlasov stochastic differential equations with super-linear coefficients, achieving strong convergence under non-globally Lipschitz conditions.

Contribution

It introduces novel numerical schemes for McKean-Vlasov SDEs with super-linear growth, proving their convergence and validating with numerical experiments.

Findings

Half-order strong convergence of the methods

Full convergence rate established via propagation of chaos

Numerical experiments confirm theoretical results

Abstract

We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the drift and diffusion coefficients. Under certain non-globally Lipschitz conditions, the proposed numerical approaches have half-order convergence in the strong sense to the corresponding system of interacting particles associated with McKean-Vlasov SDEs. By leveraging a result on the propagation of chaos, we establish the full convergence rate of the modified Euler approximations to the solution of the McKean-Vlasov SDEs. Numerical experiments are included to validate the theoretical results.