Limit theorems for monotone Markov processes

Rabindra N Bhattacharya, Mukul Majumdar, Nigar Hashimzade

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 A
Volume72
Issue number1
DOIs
StatePublished - Feb 1 2010

Fingerprint

Limit Theorems
Markov Process
Monotone
Harris Recurrence
Rate of Convergence
Monotone Map
Total Variation Distance
Queuing Theory
Convergence to Equilibrium
Irreducibility
Central limit theorem
Economics
Metric
Polynomial
Subset
Invariant
Markov process
Rate of convergence
Limit theorems
Class

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

Limit theorems for monotone Markov processes. / Bhattacharya, Rabindra N; Majumdar, Mukul; Hashimzade, Nigar.

In: Sankhya A, Vol. 72, No. 1, 01.02.2010, p. 170-190.

Research output: Contribution to journalArticle

Bhattacharya, Rabindra N ; Majumdar, Mukul ; Hashimzade, Nigar. / Limit theorems for monotone Markov processes. In: Sankhya A. 2010 ; Vol. 72, No. 1. pp. 170-190.
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