Chains with complete connections:: General theory, uniqueness, loss of memory and mixing properties
Chains with complete connections:: General theory, uniqueness, loss of memory and mixing properties
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DOI：
10.1007/s10955-004-8821-5
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发表时间：
2005-02-01
影响因子：
1.6
通讯作者：
Maillard, G
中科院分区：
文献类型：
--
作者：
Fernández, R;Maillard, G
我们引入了一个用于研究离散时间随机过程的统计力学形式，并证明了：(i)极值链的一般性质，包括尾代数上的平凡性、短距离相关性、无限体积极限实现和遍历性。（ii）两个新的一致性链唯一性的充分条件。第一个是一维吉布斯测度的乔治准则的转录，第二个对应于统计力学中的多布鲁申准则。（iii） Dobrushin体系中链的记忆丧失和混合特性的结果。这些结果是对文献中已有结果的补充，并推广了基于Dobrushin遍历系数的马尔可夫结果。
We introduce a statistical mechanical formalism for the study of discrete-time stochastic processes with which we prove: (i) General properties of extremal chains, including triviality on the tail sigma-algebra, short-range correlations, realization via infinite-volume limits and ergodicity. (ii) Two new sufficient conditions for the uniqueness of the consistent chain. The first one is a transcription of a criterion due to Georgii for one-dimensional Gibbs measures, and the second one corresponds to the Dobrushin's criterion in statistical mechanics. (iii) Results on loss of memory and mixing properties for chains in the Dobrushin regime. These results are complementary to those existing in the literature, and generalize the Markovian results based on the Dobrushin ergodic coefficient.