Convergence and stability of modified partially truncated Euler-Maruyama method for nonlinear stochastic differential equations with Holder continuous diffusion coefficient

Recently, Yang et al. (2020) established the strong convergence of the truncated Euler-Maruyama (EM) approximation, that was first proposed by Mao (2015), for onedimensional stochastic differential equations with superlinearly growing drift and the Holder continuous diffusion coefficients. However, there are some restrictions on the truncation functions and these restrictions sometimes might force the step size to be so small that the truncated EM method would be inapplicable. The key aim of this paper is to construct several new techniques of the partially truncated EM method to establish the optimal convergence rate in theory without these restrictions. The other aim is to study the stability of the partially truncated EM method. Finally, some simulations and examples are provided to support the theoretical results and demonstrate the validity of the approach. (C) 2021 Elsevier B.V. All rights reserved.