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Positive Recurrence: Weakly Connected Ergodic Classes

  • G. George Yin
  • Chao Zhu
Chapter
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 63)

Abstract

To study the positive recurrence and ergodicity, one of the conditions used in Chapters 3 and 4 is that the states of the switching process belong to only one ergodic class. In this chapter, we further our study by treating a more general class of problems. We consider the case that the states of the discrete event process belong to several “ergodic” classes that are weakly connected. This notion is made more precise in what follows. A key idea is the use of two-time-scale formulation; see [176, 177] and many references therein.

The rest of the chapter is arranged as follows. Section 10.2 begins with the formulation. Section 10.3 focuses on hybrid diffusions whose discrete component lives in weakly connected “ergodic” (irreducible) classes. Finally, the chapter is concluded with additional remarks in Section 10.4.

Keywords

Markov Chain Discrete Event Transient State Limit System Switching Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitUSA
  2. 2.Department of Mathematical SciencesUniversity of Wisconsin-MilwaukeeMilwaukeeUSA

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