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

Hu, Junhao and Mao, Wei and Mao, Xuerong (2023) Advances in nonlinear hybrid stochastic differential delay equations : existence, boundedness and stability. Automatica, 147. 110682. ISSN 0005-1098 (https://doi.org/10.1016/j.automatica.2022.110682)

[thumbnail of Hu-etal-Automatica-2022-Advances-in-nonlinear-hybrid-stochastic-differential-delay-equations]
Preview
 Text. Filename: Hu_etal_Automatica_2022_Advances_in_nonlinear_hybrid_stochastic_differential_delay_equations.pdf
Accepted Author Manuscript
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo
Download (1MB)| Preview

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.

CORE (COnnecting REpositories)