An extension of the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps

TL;DR

This paper extends the Yamada-Watanabe condition to stochastic differential equations with jumps, specifically addressing cases where small jumps are summable, thereby broadening the understanding of pathwise uniqueness in jump processes.

Contribution

It introduces an extension of the Yamada-Watanabe condition applicable to SDEs with jumps, focusing on the summability of small jumps, which was not previously covered.

Findings

Established a new criterion for pathwise uniqueness with jumps

Demonstrated the applicability of the extended condition to specific jump processes

Provided theoretical foundations for future research on SDEs with jumps

Abstract

We extend the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps, in the special case where small jumps are summable.