### 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) |
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Pages (from-to) | 1802-1809 |

Number of pages | 8 |

Journal | Annals of Applied Probability |

Volume | 14 |

Issue number | 4 |

DOIs | |

State | Published - 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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## Cite this

Bhattacharya, R., & Majumdar, M. (2004). Stability in distribution of randomly perturbed quadratic maps as Markov processes.

*Annals of Applied Probability*,*14*(4), 1802-1809. https://doi.org/10.1214/105051604000000918