This work is concerned with stability of stochastic differential delay equations with Markovian switching, where the modulating Markov chain has a large state space and is subject to both fast and slow movements. Under simple conditions, we demonstrate that if the limit systems are pth-moment exponentially stable, then the original systems are pth-moment exponentially stable in an appropriate sense. In addition, the exponential stability is also investigated. Moreover, stability in distribution is obtained for such hybrid systems. © 2010 Elsevier Inc.
Yuan, C., & Yin, G. (2010). Stability of hybrid stochastic delay systems whose discrete components have a large state space: A two-time-scale approach. Journal of Mathematical Analysis and Applications, 368(1), 103–119. https://doi.org/10.1016/j.jmaa.2010.02.053