Existence and uniqueness of solutions of SDEs with discontinuous drift and finite activity jumps

TL;DR

This paper proves the existence and uniqueness of strong solutions for multi-dimensional stochastic differential equations with discontinuous drift and finite activity jumps, addressing a complex problem in stochastic analysis.

Contribution

It establishes the first rigorous proof of strong solution existence and uniqueness for such SDEs with discontinuous drift and jumps.

Findings

Proved existence of strong solutions.

Established uniqueness of solutions.

Extended results to multi-dimensional cases.

Abstract

In this letter we prove existence and uniqueness of strong solutions to multi-dimensional SDEs with discontinuous drift and finite activity jumps.