%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 }