A Numerical Method for SDEs with Discontinuous Drift

TL;DR

This paper introduces a transformation technique for SDEs with discontinuous drift, proving existence, uniqueness, and developing a convergent numerical method based on Euler-Maruyama with order 1/2.

Contribution

It presents a novel transformation approach for analyzing and numerically solving SDEs with discontinuous drift, including convergence proof and practical examples.

Findings

Proved existence and uniqueness for a class of SDEs with discontinuous drift.

Developed a numerical method with convergence order 1/2.

Demonstrated the method's effectiveness through numerical examples.

Abstract

In this paper we introduce a transformation technique, which can on the one hand be used to prove existence and uniqueness for a class of SDEs with discontinuous drift coefficient. One the other hand we present a numerical method based on transforming the Euler-Maruyama scheme for such a class of SDEs. We prove convergence of order $1/2$. Finally, we present numerical examples.