Iterated random functions. (English) Zbl 0926.60056

Diaconis, Persi; Freedman, David

SIAM Rev. 41, No. 1, 45-76 (1999).

Summary: Iterated random functions are used to draw pictures or simulate large Ising models, among other applications. They offer a method for studying the steady state distribution of a Markov chain, and give useful bounds on rates of convergence in a variety of examples. The present paper surveys the field and presents some new examples. There is a simple unifying idea: the iterates of random Lipschitz functions converge if the functions are contracting on the average.

MSC:

60J05	Discrete-time Markov processes on general state spaces
60F05	Central limit and other weak theorems

Keywords:

Markov chains; products of random matrices; iterated function systems; coupling from the past