### Abstract

We consider the random -transformation introduced by Dajani and Kraaikamp [Random -expansions. Ergod. Th. & Dynam. Sys. 23 (2003), 461-479], which is defined on . We give an explicit formula for the density function of a unique -invariant probability measure absolutely continuous with respect to the product measure , where is the -Bernoulli measure on and is the normalized Lebesgue measure on . We apply the explicit formula for the density function to evaluate its upper and lower bounds and to investigate its continuity as a function of the two parameters and .

Original language | English |
---|---|

Pages (from-to) | 1099-1120 |

Number of pages | 22 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 39 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2019 Apr 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Invariant density functions of random β-transformations.** / Suzuki, Shintaro.

Research output: Contribution to journal › Article

*Ergodic Theory and Dynamical Systems*, vol. 39, no. 4, pp. 1099-1120. https://doi.org/10.1017/etds.2017.64

}

TY - JOUR

T1 - Invariant density functions of random β-transformations

AU - Suzuki, Shintaro

PY - 2019/4/1

Y1 - 2019/4/1

N2 - We consider the random -transformation introduced by Dajani and Kraaikamp [Random -expansions. Ergod. Th. & Dynam. Sys. 23 (2003), 461-479], which is defined on . We give an explicit formula for the density function of a unique -invariant probability measure absolutely continuous with respect to the product measure , where is the -Bernoulli measure on and is the normalized Lebesgue measure on . We apply the explicit formula for the density function to evaluate its upper and lower bounds and to investigate its continuity as a function of the two parameters and .

AB - We consider the random -transformation introduced by Dajani and Kraaikamp [Random -expansions. Ergod. Th. & Dynam. Sys. 23 (2003), 461-479], which is defined on . We give an explicit formula for the density function of a unique -invariant probability measure absolutely continuous with respect to the product measure , where is the -Bernoulli measure on and is the normalized Lebesgue measure on . We apply the explicit formula for the density function to evaluate its upper and lower bounds and to investigate its continuity as a function of the two parameters and .

UR - http://www.scopus.com/inward/record.url?scp=85062223385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062223385&partnerID=8YFLogxK

U2 - 10.1017/etds.2017.64

DO - 10.1017/etds.2017.64

M3 - Article

AN - SCOPUS:85062223385

VL - 39

SP - 1099

EP - 1120

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 4

ER -