Splitting intervals

Given an interval we choose a point in the interval and one of the two subintervals thus obtained in a symmetric random manner. The process is repeated ad infinitum. We study the limiting distribution of the midpoint of the interval.

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Bibliographic Details
Published in:Statistics & probability letters 1988-07, Vol.7 (1), p.3-7
Main Author: Herz, Carl
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fourier transform
Geometric probability. Stochastic geometry. Random sets
limit laws
limit laws Mellin transform Fourier transform Tauberian theorems
Mathematics
Mellin transform
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Tauberian theorems
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Description
Summary:Given an interval we choose a point in the interval and one of the two subintervals thus obtained in a symmetric random manner. The process is repeated ad infinitum. We study the limiting distribution of the midpoint of the interval.
ISSN:0167-7152
1879-2103
DOI:10.1016/0167-7152(88)90078-8