Singular Distribution Functions for Random Variables with Stationary Digits

被引：0

作者：

Cornean, Horia ^{[1
]}

Herbst, Ira W. ^{[2
]}

Moller, Jesper ^{[1
]}

Stottrup, Benjamin B. ^{[1
]}

Sorensen, Kasper S. ^{[1
]}

机构：

[1] Aalborg Univ, Dept Math Sci, DK-9220 Aalborg, Denmark

[2] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2023年 / 25卷 / 01期

关键词：

Digit expansions of random variables in different bases; Law of pure types; Markov chain; Mixture distribution; Renewal process;

D O I：

10.1007/s11009-023-09989-y

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let F be the cumulative distribution function (CDF) of the base-q expansion n-expressionry sumexpressiontion (infinity)(n=1)X(n)q(-n) , where q >= 2 is an integer and {X-n}(n >= 1 )is a stationary stochastic process with state space {0,...,q-1} . In a previous paper we characterized the absolutely continuous and the dis-crete components of F. In this paper we study special cases of models, including stationary Markov chains of any order and stationary renewal point processes, where we establish a law of pure types: F is then either a uniform or a singular CDF on [0, 1]. Moreover, we study mixtures of such models. In most cases expressions and plots of F are given

引用

页数：26

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