RATES OF CONVERGENCE FOR EVERYWHERE-POSITIVE MARKOV-CHAINS

被引：22

作者：

BAXTER, JR

ROSENTHAL, JS

机构：

[1] UNIV MINNESOTA,SCH MATH,MINNEAPOLIS,MN 55455

[2] UNIV TORONTO,DEPT STAT,TORONTO,ON M5S 1A1,CANADA

来源：

STATISTICS & PROBABILITY LETTERS | 1995年 / 22卷 / 04期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

COMPACT OPERATOR; HILBERT-SCHMIDT CONDITION; GIBBS SAMPLER; MARKOV CHAIN; MONTE CARLO; GEOMETRIC CONVERGENCE; STATIONARY DISTRIBUTION;

D O I：

10.1016/0167-7152(94)00085-M

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：

We generalize and simplify a result of Schervish and Carlin (1992) concerning the convergence of Markov chains to their stationary distributions. We prove geometric convergence for any Markov chain whose transition operator is compact and has everywhere-positive density functions (with respect to some reference measure). We also provide, without requiring compactness, a quantitative estimate of the convergence rate, given in terms of the stationary distribution.

引用

页码：333 / 338

页数：6

共 50 条

[31] FUNCTIONS OF MARKOV-CHAINS
ROSENBLATT, M
[J]. ANNALS OF MATHEMATICAL STATISTICS, 1958, 29 (04): : 1291 - 1291
[32] MARKOV-CHAINS IN GEOLOGY
SYSKI, R
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1984, 17 (01) : 17 - 17
[33] AGGREGATION OF MARKOV-CHAINS
BOUCHERIE, RJ
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1993, 45 (01) : 95 - 114
[34] GEOMETRIC MARKOV-CHAINS
RISING, W
[J]. JOURNAL OF APPLIED PROBABILITY, 1995, 32 (02) : 349 - 374
[35] ON REGULAR MARKOV-CHAINS
ROSE, NJ
[J]. AMERICAN MATHEMATICAL MONTHLY, 1985, 92 (02): : 146 - 146
[36] TRANSFORMERS OF MARKOV-CHAINS
LORENC, AA
[J]. INFORMATION AND CONTROL, 1976, 31 (04): : 295 - 311
[37] IMPROVED BOUNDS FOR MIXING RATES OF MARKOV-CHAINS AND MULTICOMMODITY FLOW
SINCLAIR, A
[J]. LECTURE NOTES IN COMPUTER SCIENCE, 1992, 583 : 474 - 487
[38] MARKOV-CHAINS AND MARKOV REWARD MODELS
不详
[J]. COMPUTER, 1991, 24 (05) : 38 - 38
[39] POSITIVE MATRICES AND DIMENSION GROUPS AFFILIATED TO TOPOLOGICAL MARKOV-CHAINS
HANDELMAN, D
[J]. PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS, 1982, 38 : 191 - 194
[40] CONVERGENCE TO DIFFUSION PROCESSES OF MARKOV-CHAINS RELATED TO POPULATION-GENETICS
OKADA, N
[J]. ADVANCES IN APPLIED PROBABILITY, 1979, 11 (04) : 673 - 700

← 1 2 3 4 5 →