Convergence rate in [formula omitted] sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean–Vlasov equations

Abstract

This paper focuses on the numerical scheme of highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equation (NMSMVE) by virtue of the stochastic particle method. First, under general assumptions, the results about propagation of chaos in Lp sense are revealed, where the convergence rate loses a little due to the proof technique. Then the tamed Euler–Maruyama scheme to the corresponding particle system is established and the convergence rate in Lp sense is obtained. Furthermore, combining these two results gives the convergence error in Lp sense 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.