Convergence rate in $\mathcal{L}^p$ sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equations

TL;DR

This paper develops and analyzes a tamed Euler-Maruyama scheme for highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equations, establishing convergence rates and demonstrating effectiveness through numerical examples.

Contribution

It introduces a novel tamed Euler-Maruyama scheme for NMSMVE and proves its convergence rate in $ ext{L}^p$ sense, linking error to particle number and step size.

Findings

Proven propagation of chaos in $ ext{L}^p$ sense.

Established convergence rate of the scheme.

Numerical examples confirm theoretical results.

Abstract

This paper focuses on the numerical scheme of highly nonlinear neutral multiple-delay stohchastic McKean-Vlasov equation (NMSMVE) by virtue of the stochastic particle method. First, under general assumptions, the results about propagation of chaos in $\mathcal{L}^p$ sense are shown. Then the tamed Euler-Maruyama scheme to the corresponding particle system is established and the convergence rate in $\mathcal{L}^p$ sense is obtained. Furthermore, combining these two results gives the convergence error between the objective NMSMVE and numerical approximation, which is related to the particle number and step size. Finally, two numerical examples are provided to support the finding.