Limit theorems for monotone Markov processes

Rabi Bhattacharya, Mukul Majumdar, Nigar Hashimzade

Research output: Contribution to journalArticle

7 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)170-190
Number of pages21
JournalSankhya: The Indian Journal of Statistics
Volume72
Issue number1
DOIs
StatePublished - Jun 8 2010

Keywords

  • Coupling
  • Markov processes
  • Monotone i.i.d. maps
  • Polynomial convergence rates

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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