The truncated $θ$-Milstein method for nonautonomous and highly nonlinear stochastic differential delay equations

Abstract

This paper focuses on the strong convergence of the truncated θ-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate, which is close to one, is given under the weaker assumption than the monotone condition. To verify our theoretical findings, we present a numerical example.