On a Class of Stable Random Dynamical Systems: Theory and Applications

Rabi Bhattacharya, Mukul Majumdar

Research output: Contribution to journalArticle

21 Scopus citations

Abstract

We consider a random dynamical system in which the state space is an interval, and possible laws of motion are monotone functions. It is shown that if the Markov process generated by this system satisfies a splitting condition, it converges to a unique invariant distribution exponentially fast in the Kolmogorov distance. A central limit theorem on the time-averages of observed values of the states is also proved. As an application we consider a system that captures an interaction of growth and cyclical forces: of two possible laws, one is monotone, but the other is unimodal with two periodic points. Journal of Economic Literature Classification Numbers: C6, D9.

Original languageEnglish (US)
Pages (from-to)208-229
Number of pages22
JournalJournal of Economic Theory
Volume96
Issue number1-2
DOIs
StatePublished - Jan 1 2001

Keywords

  • Stability; dynamical systems; growth; cycles

ASJC Scopus subject areas

  • Economics and Econometrics

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