### 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 language | English (US) |
---|---|

Pages (from-to) | 208-229 |

Number of pages | 22 |

Journal | Journal of Economic Theory |

Volume | 96 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 2001 |

Externally published | Yes |

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### Keywords

- Stability; dynamical systems; growth; cycles

### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

*Journal of Economic Theory*,

*96*(1-2), 208-229. https://doi.org/10.1006/jeth.1999.2627

**On a Class of Stable Random Dynamical Systems : Theory and Applications.** / Bhattacharya, Rabindra N; Majumdar, Mukul.

Research output: Contribution to journal › Article

*Journal of Economic Theory*, vol. 96, no. 1-2, pp. 208-229. https://doi.org/10.1006/jeth.1999.2627

}

TY - JOUR

T1 - On a Class of Stable Random Dynamical Systems

T2 - Theory and Applications

AU - Bhattacharya, Rabindra N

AU - Majumdar, Mukul

PY - 2001/1

Y1 - 2001/1

N2 - 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.

AB - 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.

KW - Stability; dynamical systems; growth; cycles

UR - http://www.scopus.com/inward/record.url?scp=0012682611&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012682611&partnerID=8YFLogxK

U2 - 10.1006/jeth.1999.2627

DO - 10.1006/jeth.1999.2627

M3 - Article

VL - 96

SP - 208

EP - 229

JO - Journal of Economic Theory

JF - Journal of Economic Theory

SN - 0022-0531

IS - 1-2

ER -