Approximation for non-smooth functionals of stochastic differential equations with irregular drift

TL;DR

This paper investigates the weak convergence rates of the Euler-Maruyama scheme for SDEs with irregular drift, providing new approximation results for non-smooth functionals and reflected SDEs.

Contribution

It introduces a systematic method to analyze weak convergence for SDEs with irregular drift, extending to non-smooth functionals and reflected SDEs.

Findings

Established weak convergence rates for irregular drift SDEs

Derived approximation rates for non-smooth functionals

Extended results to reflected SDEs with Hölder continuous drift

Abstract

This paper aims at developing a systematic study for the weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to obtain the rates of approximation for the expectation of various non-smooth functionals of both stochastic differential equations and killed diffusion. We also apply our method to the study of the weak approximation of reflected stochastic differential equations whose drift is H\"older continuous.