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

Zhu, C.; Yin, G.

SIAM J. Control Optim. 46, No. 4, 1155-1179 (2007).

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

Keywords:

switching diffusion; Lyapunov function; weak stochastic stability; positive recurrence; ergodicity