Strong convergence rates of modified truncated EM method for stochastic differential equations

TL;DR

This paper introduces a modified truncated Euler-Maruyama method for stochastic differential equations, demonstrating improved convergence properties under weaker conditions compared to previous methods.

Contribution

The paper develops a new explicit numerical scheme with proven strong convergence rates, extending the truncated EM method with weaker assumptions.

Findings

Strong convergence to exact solutions at fixed time T

Convergence over the interval [0,T] under weaker conditions

Numerical examples confirm theoretical results

Abstract

Motivated by truncated EM method introduced by Mao (2015), a new explicit numerical method named modified truncated Euler-Maruyama method is developed in this paper. Strong convergence rates of the given numerical scheme to the exact solutions to stochastic differential equations are investigated under given conditions in this paper. Compared with truncated EM method, the given numerical simulation strongly converges to the exact solution at fixed time $T$ and over a time interval $[0,T]$ under weaker sufficient conditions. Meanwhile, the convergence rates are also obtained for both cases. Two examples are provided to support our conclusions.