Euler approximation and stability of the solution to stochastic differential equations with jumps under pathwise uniqueness

Abstract

In this paper, we consider a stochastic differential equation with jumps for which pathwise uniqueness hold. We establish a fundamental mean square convergence theorem for the Euler approximation scheme. We provide some results on strong stability with respect to small perturbations of the initial conditions, and we study the convergence of Picard approximations.

Keywords:

• Stochastic differential equations
• Euler approximation
• stability
• pathwise uniqueness
• Skorokhod selection's theorem
• Krylov type estimate

Acknowledgments

The authors wish to express their sincere gratitude to the Editor-in-Chief for following up on the article, and gratefully acknowledge the many helpful suggestions and valuable comments of the Reviewers that lead to an improved paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).