A composition structure is a sequence of consistent probability
distributions for compositions (ordered partitions) of $n = 1, 2, \dots$. Any
composition structure can be associated with an exchangeable random composition
of the set of natural numbers. Following Donnelly and Joyce, we study the
problem of characterizing a generic composition structure as a convex mixture
of the "extreme" ones. We topologize the family $\mathscr{U}$ of open subsets
of [0, 1] so that $\mathscr{U}$ becomes compact and show that $\mathscr{U}$ is
homeomorphic to the set of extreme composition structures. The general
composition struc-ture is related to a random element of $\mathscr{U}$ via a
construction introduced by J. Pitman.
Publié le : 1997-07-14
Classification:
Composition structure,
partition structure,
exchangeability,
paintbox process,
random set,
60G09,
60C05,
60J50
@article{1024404519,
author = {Gnedin, Alexander V.},
title = {The representation of composition structures},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 1437-1450},
language = {en},
url = {http://dml.mathdoc.fr/item/1024404519}
}
Gnedin, Alexander V. The representation of composition structures. Ann. Probab., Tome 25 (1997) no. 4, pp. 1437-1450. http://gdmltest.u-ga.fr/item/1024404519/