On Strong Feller, Recurrence, and Weak Stabilization of Regime-Switching Diffusions

Authors:
C. Zhu;G. Yin
Affiliations:
zhu@uwm.edu;-
Venue:
SIAM Journal on Control and Optimization
Year:
2009

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Abstract

Focusing on two-component Markov processes having continuous dynamics and discrete events, this work develops 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, easily verifiable conditions are established. Also provided are conditions for null-recurrent processes. Furthermore, conditions for controlled switching diffusions in which the feedback controls ensure weak stability (or ergodicity) are given. Finally, simple examples are used for demonstration.