Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift

作者：

Highlights：

• The first existence and uniqueness result for jump-diffusion SDEs with discontinuous drift.

• The first approximation result for solutions to such SDEs (We obtain the optimal L2-order 1/2 for the EM scheme.).

• Significant extension, comparing to the existing ones, of the theoretical methods used in the proof of the results mentioned above.

• Theoretical results supported by numerical experiments.

摘要

•The first existence and uniqueness result for jump-diffusion SDEs with discontinuous drift.•The first approximation result for solutions to such SDEs (We obtain the optimal L2-order 1/2 for the EM scheme.).•Significant extension, comparing to the existing ones, of the theoretical methods used in the proof of the results mentioned above.•Theoretical results supported by numerical experiments.

论文关键词：Jump-diffusion stochastic differential equation,Discontinuous drift,Existence and uniqueness,Euler–Maruyama scheme,Strong convergence rate

论文评审过程：Received 21 April 2020, Revised 14 January 2021, Accepted 9 March 2021, Available online 25 March 2021, Version of Record 25 March 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126191