Alternative characterization of ergodicity for doubly stochastic chains

Behrouz Touri, Angelia Nedic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we discuss the ergodicity of stochastic and doubly stochastic chains. We define absolute infinite flow property and show that this property is necessary for ergodicity of any stochastic chain. The proof is constructive and makes use of a rotational transformation, which we introduce and study. We then focus on doubly stochastic chains for which we prove that the absolute infinite flow property and ergodicity are equivalent. The proof of this result makes use of a special decomposition of a doubly stochastic matrix, as given by Birkhoff-von Neumann theorem. Finally, we show that a backward product of doubly stochastic matrices is convergent up to a permutation sequence and, as a result, the set of accumulation points of such a product is finite.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages5371-5376
Number of pages6
DOIs
StatePublished - Dec 1 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1112/15/11

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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  • Cite this

    Touri, B., & Nedic, A. (2011). Alternative characterization of ergodicity for doubly stochastic chains. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 5371-5376). [6161372] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2011.6161372