Pathwise Uniqueness for SDEs with Singular Drift and Nonconstant Diffusion: A simple proof

TL;DR

This paper presents a simplified proof of pathwise uniqueness for stochastic differential equations with Sobolev diffusion and integrable drift, extending previous methods to cases with nonconstant diffusion coefficients.

Contribution

It introduces a new, simpler proof technique for pathwise uniqueness in SDEs with nonconstant diffusion and singular drift, building on prior work.

Findings

Extended the method of Fedrizzi and Flandoli to nonconstant diffusion cases

Provided a more straightforward proof of pathwise uniqueness

Applicable to SDEs with Sobolev diffusion and integrable drift

Abstract

A new proof of pathwise uniqueness for SDEs with Sobolev diffusion and integrable drift term is introduced by extending a method from E. Fedrizzi and F. Flandoli (Pathwise uniqueness and continuous dependence of SDEs with non-regular drift, Stochastics 83 (2011), pp. 241--257) to the case of nonconstant diffusion.