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Sankhya A

, Volume 72, Issue 1, pp 170–190 | Cite as

Limit theorems for monotone Markov processes

  • Rabi Bhattacharya
  • Mukul Majumdar
  • Nigar Hashimzade
Article

Abstract

This article considers the convergence to steady states of Markov processes generated by the action of successive i.i.d. monotone maps on a subset S of an Eucledian space. Without requiring irreducibility or Harris recurrence, a “splitting” condition guarantees the existence of a unique invariant probability as well as an exponential rate of convergence to it in an appropriate metric. For a special class of Harris recurrent processes on [0,∞) of interest in economics, environmental studies and queuing theory, criteria are derived for polynomial and exponential rates of convergence to equilibrium in total variation distance. Central limit theorems follow as consequences.

Keywords and phrases

Markov processes coupling monotone i.i.d. maps polynomial convergence rates 

AMS (2000) subject classification

Primary 60F05, 60J05 

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Copyright information

© Indian Statistical Institute 2010

Authors and Affiliations

  • Rabi Bhattacharya
    • 1
    • 4
  • Mukul Majumdar
    • 2
    • 5
  • Nigar Hashimzade
    • 3
    • 6
  1. 1.The University of ArizonaTucsonUSA
  2. 2.Cornell UniversityIthacaUSA
  3. 3.University of ReadingReadingUK
  4. 4.Department of MathematicsThe University of ArizonaTucsonUSA
  5. 5.Department of EconomicsCornell UniversityIthacaUSA
  6. 6.School of EconomicsUniversity of ReadingReadingUK

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