Convergence Rates for the Truncated Euler-Maruyama Method for Nonlinear Stochastic Differential Equations

Abstract

In this paper, our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients. When the diffusion coefficient is polynomially growing or linearly growing, the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval [0, T ], respectively. In both situations, the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required. Two examples are provided to illustrate the theory.