This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, which has been popular in the economics and genetics literatures. We construct a joint agent-probability space, and randomized mutation, partial matching and match-induced type-changing functions that satisfy appropriate independence conditions. The proofs are achieved via nonstandard analysis. The proof for the dynamic setting relies on a new Fubini-type theorem for an infinite product of Loeb transition probabilities, based on which a continuum of independent Markov chains is derived from random mutation, random partial matching and random type changing.
Publié le : 2007-02-14
Classification:
Random matching,
independence,
types,
Markov chains,
mutation,
60J05,
91B68,
60A10
@article{1171377188,
author = {Duffie, Darrell and Sun, Yeneng},
title = {Existence of independent random matching},
journal = {Ann. Appl. Probab.},
volume = {17},
number = {1},
year = {2007},
pages = { 386-419},
language = {en},
url = {http://dml.mathdoc.fr/item/1171377188}
}
Duffie, Darrell; Sun, Yeneng. Existence of independent random matching. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp. 386-419. http://gdmltest.u-ga.fr/item/1171377188/