### 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 | |

State | Published - Nov 2004 |

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### Keywords

- Invariant probability
- Markov process
- Quadratic maps

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Annals of Applied Probability*,

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

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

Research output: Contribution to journal › Article

*Annals of Applied Probability*, vol. 14, no. 4, pp. 1802-1809. https://doi.org/10.1214/105051604000000918

}

TY - JOUR

T1 - Stability in distribution of randomly perturbed quadratic maps as Markov processes

AU - Bhattacharya, Rabindra N

AU - Majumdar, Mukul

PY - 2004/11

Y1 - 2004/11

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=26844551347&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26844551347&partnerID=8YFLogxK

U2 - 10.1214/105051604000000918

DO - 10.1214/105051604000000918

M3 - Article

AN - SCOPUS:26844551347

VL - 14

SP - 1802

EP - 1809

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 4

ER -