Convergence rate of truncated EM method for periodic stochastic differential equations in superlinear scenario

Abstract

Periodicity has been widely recognised in a variety of areas including biology, finance and control theory. As an important class of non-autonomous SDEs, stochastic differential equations (SDEs) with periodic coefficients have thus been receiving great attention recently. In this paper, we study the strong convergence of the truncated Euler–Maruyama (EM) method to the superlinear SDEs with periodic coefficients and generate an almost optimal convergence rate of order close to $1/2$. Due to the typical features of such SDEs including periodicity and super-linearity, this work becomes challenging and non-trivial. Finally our theory is demonstrated by computer simulations.