### 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 |
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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