Convergence of Modified Truncated Euler-Maruyama Method for Stochastic Differential Equations with Hölder Diffusion Coefficients

Abstract

Convergence of modified truncated Euler-Maruyama (MTEM) method for stochastic differential equations (SDEs) with $(1/2 + α)$-Hölder continuous diffusion coefficients are investigated in this paper. We prove that the MTEM method for SDE converges to the exact solution in $L^q$ sense under given conditions. Two examples are provided to support our conclusions.