Invariant density functions of random β-transformations

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1099-1120
Number of pages22
JournalErgodic Theory and Dynamical Systems
Volume39
Issue number4
DOIs
Publication statusPublished - 2019 Apr 1
Externally publishedYes

Fingerprint

Density Function
Probability density function
Explicit Formula
Product Measure
Invariant
Lebesgue Measure
Absolutely Continuous
Bernoulli
Invariant Measure
Probability Measure
Two Parameters
Upper and Lower Bounds
Evaluate

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Ergodic Theory and Dynamical Systems, Vol. 39, No. 4, 01.04.2019, p. 1099-1120.

Research output: Contribution to journalArticle

@article{d9bf245204134651855ad2300451984b,
title = "Invariant density functions of random β-transformations",
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 .",
author = "Shintaro Suzuki",
year = "2019",
month = "4",
day = "1",
doi = "10.1017/etds.2017.64",
language = "English",
volume = "39",
pages = "1099--1120",
journal = "Ergodic Theory and Dynamical Systems",
issn = "0143-3857",
publisher = "Cambridge University Press",
number = "4",

}

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 -