This work is devoted to stability of regime-switching diffusion processes. After presenting the formulation of regime-switching diffusions, the notion of stability is recalled, and necessary conditions for p-stability are obtained. Then main results on stability and instability for systems...

Markov chains have been frequently used to characterize uncertainty in many real-world problems. Quite often, these Markov chains can be decomposed into a vector consisting of fast and slow components; these components are coupled through weak and strong interactions. The main goal of this work...

A differential delay equation with a small parameter and random noise perturbations is considered in this paper. Asymptotic properties are developed. The martingale averaging techniques are adopted to treat our problem, and the method of weak convergence is employed. The random fluctuation is...