Stability in distribution of randomly perturbed quadratic maps as Markov processes

Rabi Bhattacharya; Mukul Majumdar

doi:10.1214/105051604000000918

Stability in distribution of randomly perturbed quadratic maps as Markov processes

Rabi Bhattacharya
, Mukul Majumdar

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1802-1809
Number of pages	8
Journal	Annals of Applied Probability
Volume	14
Issue number	4
DOIs	https://doi.org/10.1214/105051604000000918
State	Published - Nov 2004
Externally published	Yes

Keywords

Invariant probability
Markov process
Quadratic maps

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/105051604000000918

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AB - 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.

KW - Invariant probability

KW - Markov process

KW - Quadratic maps

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Stability in distribution of randomly perturbed quadratic maps as Markov processes

Abstract

Keywords

ASJC Scopus subject areas

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