Title :
Feller continuity, recurrence, and stabilization of regime-switching diffusions
Author :
Zhu, C. ; Yin, G.
Author_Institution :
Dept. of Math. Sci., Univ. of Wisconsin-Milwaukee, Milwaukee, WI, USA
Abstract :
This work is based on our results in. Dealing with two-component Markov processes having continuous dynamics and discrete events, we develop asymptotic properties of regime-switching diffusions. First, strong Feller property is established. Next, classifying the underlying processes as recurrence (positive recurrence or null recurrence) or transience, sufficient conditions for such processes are obtained. In addition to providing general criteria for recurrent and transient switching diffusions, for processes that are linearizable with respect to the continuous component, we establish easily verifiable conditions. Furthermore, we provide conditions for controlled switching diffusions in which the feedback controls ensure weak stability (or ergodicity). Finally, we give a simple example to demonstrate the results.
Keywords :
Markov processes; discrete event systems; feedback; stability; time-varying systems; Feller continuity; Feller recurrence; continuous dynamics; controlled switching diffusions; discrete events; feedback controls; regime-switching diffusion stabilization; two-component Markov processes; Diffusion processes; Feedback control; Markov processes; Switches; Transient analysis; Regime-switching diffusion; linearizable system; null recurrence; positive recurrence; recurrence; strong Feller property; transience; weak stabilization;
Conference_Titel :
Decision and Control (CDC), 2010 49th IEEE Conference on
Conference_Location :
Atlanta, GA
Print_ISBN :
978-1-4244-7745-6
DOI :
10.1109/CDC.2010.5717587