Markov Chains and Mappings of Distributions on Compact Spaces

被引：0

作者：

Aldous, David J. ^{[1
]}

Feng, Shi ^{[2
]}

机构：

[1] Univ Calif Berkeley, Dept Stat, 367 Evans Hall 3860, Berkeley, CA 94720 USA

[2] Cornell Univ, Dept Math, Ithaca, NY USA

来源：

ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS | 2024年 / 21卷

关键词：

Coupling; Markov chain; compact metric space; dynamical system;

D O I：

10.30757/ALEA.v21-53

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Consider a compact metric space S and a pair (j,k) with k >= 2 and 1 <= j <= k. For any probability distribution theta is an element of P(S), define a Markov chain on S by: from state s, take k i.i.d. (theta) samples, and jump to the j'th closest. Such a chain converges in distribution to a unique stationary distribution, say pi(j,k)(theta). So this defines a mapping pi(j,k ): P(S)-> P(S). What happens when we iterate this mapping? In particular, what are the fixed points of this mapping? We present a few rigorous results, to complement our extensive simulation study elsewhere.

引用

页码：1407 / 1416

页数：10