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

Abstract

In this paper we propose and analyze a truncated θ-Milstein method for solving a class of non-autonomous stochastic differential delay equations with highly nonlinear coefficients. Under a generalized monotone condition of the coefficients, the convergence order of the truncated θ-Milstein method is obtained. We find that the convergence rate is dependent on the exponent of the Hölder conditions. To verify our theoretical findings, we provide a numerical example.