Stability in distribution of randomly perturbed quadratic maps as Markov processes

Rabindra N Bhattacharya, Mukul Majumdar

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 2004

Fingerprint

Quadratic Map
Markov Process
Harris Recurrence
Positive Recurrence
Markov Model
Parameter Space
Economics
Iteration
Uncertainty
Optimization
Markov process
Markov model

Keywords

  • Invariant probability
  • Markov process
  • Quadratic maps

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Stability in distribution of randomly perturbed quadratic maps as Markov processes. / Bhattacharya, Rabindra N; Majumdar, Mukul.

In: Annals of Applied Probability, Vol. 14, No. 4, 11.2004, p. 1802-1809.

Research output: Contribution to journalArticle

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