For the past few decades, the stability criteria for the stochastic differential delay equations (SDDEs) have been studied intensively. Most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability criterion for highly nonlinear hybrid stochastic differential equations is investigated in Fei et al. (2017). In this paper, we investigate a class of highly nonlinear hybrid stochastic integro-differential delay equations (SIDDEs). First, we establish the stability and boundedness of hybrid stochastic integro-differential delay equations. Then the delay-dependent criteria of the stability and boundedness of solutions to SIDDEs are studied. Finally, an illustrative example is provided.
- stochastic integro-differential delay equation (SIDDE)
- nonlinear growth condition
- asymptotic stability
- Markovian switching
- Lyapunov functional
Fei, C., Shen, M., Fei, W., Mao, X., & Yan, L. (2019). Stability of highly nonlinear hybrid stochastic integro-differential delay equations. Nonlinear Analysis: Hybrid Systems, 31, 180-199. https://doi.org/10.1016/j.nahs.2018.09.001