×

Iterated random functions. (English) Zbl 0926.60056

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
PDFBibTeX XMLCite
Full Text: DOI