Explicit Numerical Approximations for McKean-Vlasov Neutral Stochastic Differential Delay Equations

TL;DR

This paper develops and analyzes a numerical scheme for approximating solutions to McKean-Vlasov neutral stochastic differential delay equations with super-linear drift growth, ensuring convergence and providing error estimates.

Contribution

It introduces a tamed Euler-Maruyama scheme combined with particle methods for MV-NSDDEs, establishing convergence rates under super-linear growth conditions.

Findings

Existence and uniqueness of solutions for MV-NSDDEs.

Convergence of the numerical scheme with explicit error bounds.

Effective approximation of the law via particle methods.

Abstract

This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that the solution of MV-NSDDE exists and is unique. Then, we use a stochastic particle method, which is on the basis of the results about the propagation of chaos between particle system and the original MV-NSDDE, to deal with the approximation of the law. Furthermore, we construct the tamed Euler-Maruyama numerical scheme with respect to the corresponding particle system and obtain the rate of convergence. Combining propagation of chaos and the convergence rate of the numerical solution to the particle system, we get a convergence error between the numerical solution and exact solution of the original MV-NSDDE in the stepsize and number of particles.