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Stability of regime-switching diffusions. (English) Zbl 1119.60065
Summary: 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 arising in approximation are presented. Easily verifiable conditions are established. An example is examined as a demonstration. A remark on linear systems is also provided.

60J60 Diffusion processes
60J27 Continuous-time Markov processes on discrete state spaces
93E15 Stochastic stability in control theory
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