Self-similar and Markov composition structures
| dc.creator | Gnedin, Alexander | |
| dc.creator | Pitman, Jim | |
| dc.date | 2005-05-31 | |
| dc.date.accessioned | 2026-07-07T05:20:24Z | |
| dc.date.available | 2026-07-07T05:20:24Z | |
| dc.description | 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. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505687 | |
| dc.identifier | http://arxiv.org/abs/math/0505687 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75368 | |
| dc.subject | Probability | |
| dc.subject | 60G09, 60C05 | |
| dc.title | Self-similar and Markov composition structures | |
| dc.type | text |