Unique strong solutions of Levy processes driven stochastic differential equations with discontinuous coefficients

TL;DR

This paper proves the existence and uniqueness of strong solutions for one-dimensional stochastic differential equations driven by Brownian motion and Levy processes, even with discontinuous coefficients, using weak uniqueness and local time methods.

Contribution

It introduces new conditions ensuring strong solutions for SDEs driven by Levy processes with discontinuous coefficients, expanding existing theoretical frameworks.

Findings

Established pathwise uniqueness under general conditions

Applied local time techniques to Levy-driven SDEs

Extended solution theory to discontinuous coefficients

Abstract

We establish the existence and uniqueness for a one-dimensional stochastic differential equation driven by a Brownian motion and a pure jump {\levy} process. It is shown that under fairly general conditions on the coefficients, pathwise uniqueness holds based on the methods of weak uniqueness and local time technique.