Euler-Maruyama scheme for SDEs with Dini continuous coefficients

TL;DR

This paper establishes the convergence rate of the Euler-Maruyama scheme for non-degenerate SDEs with Dini continuous coefficients, using the regularity of the Kolmogorov equation solution and simplifying previous proofs.

Contribution

It introduces a simplified proof method for convergence rates of Euler-Maruyama schemes under Dini continuity, weakening previous conditions and leveraging Taylor expansion.

Findings

Convergence rate of Euler-Maruyama scheme for Dini continuous coefficients.

Simplified proof approach reduces complexity of previous methods.

Weakening of conditions compared to prior work.

Abstract

In this paper, we show the convergence rate of Euler-Maruyama scheme for non-degenerate SDEs with Dini continuous coefficients, by the aid of the regularity of the solution to the associated Kolmogorov equation. We obtain the same conclusions using a simple and clever way to simplify the proof and weaken the conditions in \cite{BHY} by the properties of Dini continuous and Taylor expansion.