# Pathwise uniqueness for stochastic differential equations driven by pure jump processes

## TL;DR

This paper establishes conditions under which pathwise uniqueness holds for one-dimensional stochastic differential equations driven by pure jump processes, bridging the gap between weak and strong solutions using Tanaka's formula and local time techniques.

## Contribution

It provides new conditions ensuring pathwise uniqueness for SDEs with pure jump processes, extending previous results by connecting weak and strong solution concepts.

## Key findings

- Pathwise uniqueness is proven under specific coefficient conditions.
- No gap exists between weak and strong uniqueness for these SDEs.
- The approach uses Tanaka's formula and local time methods.

## Abstract

Based on the weak existence and weak uniqueness, we study the pathwise uniqueness of the solutions for a class of one-dimensional stochastic differential equations driven by pure jump processes. By using Tanaka's formula and the local time technique, we show that there is no gap between the strong uniqueness and weak uniqueness when the coefficients of the Poisson random measures satisfy a suitable condition