Iterated random functions

被引：420

作者：

Diaconis, P ^{[1
]}

Freedman, D

机构：

[1] Stanford Univ, Dept Math & Stat, Stanford, CA 94305 USA

[2] Univ Calif Berkeley, Dept Stat, Berkeley, CA 94720 USA

来源：

SIAM REVIEW | 1999年 / 41卷 / 01期

关键词：

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

D O I：

10.1137/S0036144598338446

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：45 / 76

页数：32

共 76 条

[21]

BRANDT A, 1990, STATIONARY STOCHASTI

[22] THE STRONG LAW OF LARGE NUMBERS FOR A CLASS OF MARKOV-CHAINS [J].

BREIMAN, L .

ANNALS OF MATHEMATICAL STATISTICS, 1960, 31 (03) :801-803

[23]

BROWN K, 1997, IN PRESS ANN PROBAB

[24]

Chamayou J.-F., 1991, J THEORET PROBAB, V4, P3

[25] DISTRIBUTION-FUNCTIONS OF MEANS OF A DIRICHLET PROCESS [J].

CIFARELLI, DM ;

REGAZZINI, E .

ANNALS OF STATISTICS, 1990, 18 (01) :429-442

[26]

Crownover RM., 1995, Introduction to fractals and chaos

[27]

DIACONIS P., 1996, BAYESIAN STAT, V5, P97

[28]

DIACONIS P, 1986, CONT MATH, V50, P173

[29] MEASURABLE SETS OF MEASURES [J].

DUBINS, L ;

FREEDMAN, D .

PACIFIC JOURNAL OF MATHEMATICS, 1964, 14 (04) :1211-&

[30] INVARIANT PROBABILITIES FOR CERTAIN MARKOV PROCESSES [J].

DUBINS, LE ;

FREEDMAN, DA .

ANNALS OF MATHEMATICAL STATISTICS, 1966, 37 (04) :837-&

← 1 2 3 4 5 6 7 8 →