The bijection between composition structures and random closed subsets of the
unit interval implies that the composition structures associated with $S \cap
0,1$ for a self-similar random set $SR_+$ are those which
are consistent with respect to a simple truncation operation. Using the
standard coding of compositions by finite strings of binary digits starting
with a 1, the random composition of $n$ is defined by the first $n$ terms of a
random binary sequence of infinite length. The locations of 1s in the sequence
are the places visited by an increasing time-homogeneous Markov chain on the
positive integers if and only if $S = \exp(-W)$ for some stationary
regenerative random subset $W$ of the real line. Complementing our study in
previous papers, we identify self-similar Markovian composition structures
associated with the two-parameter family of partition structures.
%0 Generic
%1 arXiv:math.PR/0505687
%A Gnedin, Alexander
%A Pitman, Jim
%D 2005
%K author_pitman_from_arxiv
%T Self-similar and Markov composition structures.
%U http://arxiv.org/abs/math.PR/0505687
%X The bijection between composition structures and random closed subsets of the
unit interval implies that the composition structures associated with $S \cap
0,1$ for a self-similar random set $SR_+$ are those which
are consistent with respect to a simple truncation operation. Using the
standard coding of compositions by finite strings of binary digits starting
with a 1, the random composition of $n$ is defined by the first $n$ terms of a
random binary sequence of infinite length. The locations of 1s in the sequence
are the places visited by an increasing time-homogeneous Markov chain on the
positive integers if and only if $S = \exp(-W)$ for some stationary
regenerative random subset $W$ of the real line. Complementing our study in
previous papers, we identify self-similar Markovian composition structures
associated with the two-parameter family of partition structures.
@misc{arXiv:math.PR/0505687,
abstract = {The bijection between composition structures and random closed subsets of the
unit interval implies that the composition structures associated with $S \cap
[0,1]$ for a self-similar random set $S\subset {\mathbb R}_+$ are those which
are consistent with respect to a simple truncation operation. Using the
standard coding of compositions by finite strings of binary digits starting
with a 1, the random composition of $n$ is defined by the first $n$ terms of a
random binary sequence of infinite length. The locations of 1s in the sequence
are the places visited by an increasing time-homogeneous Markov chain on the
positive integers if and only if $S = \exp(-W)$ for some stationary
regenerative random subset $W$ of the real line. Complementing our study in
previous papers, we identify self-similar Markovian composition structures
associated with the two-parameter family of partition structures.},
added-at = {2008-01-25T05:29:59.000+0100},
arxiv = {arXiv:math.PR/0505687},
author = {Gnedin, Alexander and Pitman, Jim},
biburl = {https://www.bibsonomy.org/bibtex/2a0cb7cf90651222782dbacefc83bcae4/pitman},
interhash = {98785e0bcc2d7e7aa3481dfd72003560},
intrahash = {a0cb7cf90651222782dbacefc83bcae4},
keywords = {author_pitman_from_arxiv},
timestamp = {2008-01-25T05:33:08.000+0100},
title = {{Self-similar and Markov composition structures.}},
url = {http://arxiv.org/abs/math.PR/0505687},
year = 2005
}