The truncated Euler–Maruyama method for stochastic differential equations with Hölder diffusion coefficients

Abstract In stochastic financial and biological models, the diffusion coefficients often involve the term x , or more general | x | r for r ∈ ( 0 , 1 ) , which is non-Lipschitz. In this paper, we study the strong convergence of the truncated Euler–Maruyama (EM) approximation first proposed by Mao (2015) for one-dimensional stochastic differential equations (SDEs) with superlinearly growing drifts and the Holder continuous diffusion coefficients.