Stability in distribution of randomly perturbed quadratic maps as Markov processes

Rabi Bhattacharya, Mukul Majumdar

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Iteration of randomly chosen quadratic maps defines a Markov process: X n+1 = ε n+1 X n(1 - X n), where ε n are i.i.d. with values in the parameter space [0,4] of quadratic maps F θ(x) = θx(1 - x). Its study is of significance as an important Markov model, with applications to problems of optimization under uncertainty arising in economics. In this article a broad criterion is established for positive Harris recurrence of X n.

Original languageEnglish (US)
Pages (from-to)1802-1809
Number of pages8
JournalAnnals of Applied Probability
Volume14
Issue number4
DOIs
StatePublished - Nov 1 2004

Keywords

  • Invariant probability
  • Markov process
  • Quadratic maps

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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