Abstract
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.
Citation
Darrell Duffie. Yeneng Sun. "Existence of independent random matching." Ann. Appl. Probab. 17 (1) 386 - 419, February 2007. https://doi.org/10.1214/105051606000000673
Information