Weak Error for the Euler Scheme Approximation of Diffusions with Non-Smooth Coefficients *

TL;DR

This paper investigates the weak error of the Euler scheme when approximating diffusion processes with non-smooth, bounded coefficients, including H{"o}lder continuous and piecewise smooth cases, providing insights into its accuracy.

Contribution

It offers new analysis of the weak error for Euler schemes applied to diffusions with non-smooth coefficients, extending understanding beyond smooth cases.

Findings

Weak error bounds established for H{"o}lder continuous coefficients

Analysis of Euler scheme performance with piecewise smooth drifts

Insights into approximation accuracy for non-smooth diffusions

Abstract

We study the weak error associated with the Euler scheme of non degenerate diffusion processes with non smooth bounded coefficients. Namely, we consider the cases of H{\"o}lder continuous coefficients as well as piecewise smooth drifts with smooth diffusion matrices.