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Asymptotic properties of hybrid diffusion systems. (English) Zbl 1140.93045

Summary: In response to the increasing needs for control and optimization of hybrid systems, this work is concerned with such asymptotic properties as recurrence (also known as weak stochastic stability in the literature) and ergodicity of regime-switching diffusions. Using Lyapunov functions, necessary and sufficient conditions for positive recurrence are developed. Then, ergodicity of positive recurrent regime-switching diffusions is obtained by constructing cycles using the associated discrete-time Markov chains.

MSC:

93E15 Stochastic stability in control theory
93E03 Stochastic systems in control theory (general)
60J60 Diffusion processes
60J05 Discrete-time Markov processes on general state spaces
93D30 Lyapunov and storage functions
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