Advances in nonlinear hybrid stochastic differential delay equations: existence, boundedness and stability

Junhao Hu, Wei Mao, Xuerong Mao

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is concerned with a class of highly nonlinear hybrid stochastic differential delay equations (SDDEs). Different from the most existing papers, the time delay functions in the SDDEs are no longer required to be differentiable, not to mention their derivatives are less than 1. The generalized Hasminskii-type theorems are established for the existence and uniqueness of the global solutions. Comparing with the existing results, we show our new theorems are much more general and can be applied to a much wider class of highly nonlinear SDDEs. Further sufficient conditions are also obtained for the asymptotic boundedness and stability.

Original languageEnglish
Article number110682
JournalAutomatica
Volume147
Early online date31 Oct 2022
DOIs
Publication statusPublished - 31 Jan 2023

Keywords

  • stochastic differential delay equations
  • non-differentiable time delay functions
  • Hasminskii-type theorems
  • boundedness
  • stability

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