一般离散马尔可夫链渐近方差的变分公式

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2023-02-01 DOI:10.3150/21-bej1458

Lu-Jing Huang, Yong-Hua Mao

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引用次数: 0

摘要

渐近方差是评价马尔可夫链，特别是中心极限定理性能的一个重要准则。给出了广义状态空间上离散时间(不可逆)马尔可夫链渐近方差的变分公式。变分公式提供了许多应用，将经典的Peskun比较定理推广到不可逆的马尔可夫链，并得到了不同扰动下马尔可夫链之间的几个比较定理。

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Variational formulas for asymptotic variance of general discrete-time Markov chains

The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for the central limit theorems. We give the variational formulas for the asymptotic variance of discrete-time (non-reversible) Markov chains on general state space. The variational formulas provide many applications, extending the classical Peskun’s comparison theorem to non-reversible Markov chains, and obtaining several comparison theorems between Markov chains with various perturbations.

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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.