Boundedness analysis of stochastic delay differential equations with Lévy noise

作者：

Highlights：

• Both time delay and Lévy noise are taken into considered in the stochastic differential equations.

• Mean square asymptotic boundedness criteria of the solutions are established by the method of reduction and the Itô formula.

• Based on the Chebyshev inequality and the Borel–Cantelli lemma, the almost surely boundedness criteria are obtained.

摘要

•Both time delay and Lévy noise are taken into considered in the stochastic differential equations.•Mean square asymptotic boundedness criteria of the solutions are established by the method of reduction and the Itô formula.•Based on the Chebyshev inequality and the Borel–Cantelli lemma, the almost surely boundedness criteria are obtained.

论文关键词：Lévy noise,Mean square asymptotic boundedness,Almost surely asymptotic boundedness,Stochastic delay differential equations

论文评审过程：Received 7 January 2021, Revised 10 December 2021, Accepted 26 December 2021, Available online 10 January 2022, Version of Record 10 January 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126902