General Limit Distributions for Sums of Random Variables with a Matrix Product Representation

被引：2

作者：

Angeletti, Florian ^{[1
,2
]}

Bertin, Eric ^{[3
]}

Abry, Patrice ^{[4
]}

机构：

[1] Natl Inst Theoret Phys NITheP, ZA-7600 Stellenbosch, South Africa

[2] Univ Stellenbosch, Inst Theoret Phys, ZA-7600 Stellenbosch, South Africa

[3] Univ Grenoble 1, CNRS UMR 5588, Lab Interdisciplinaire Phys, F-38402 St Martin Dheres, France

[4] Univ Lyon, CNRS, ENS Lyon, Lab Phys, F-69007 Lyon, France

来源：

JOURNAL OF STATISTICAL PHYSICS | 2014年 / 157卷 / 06期

关键词：

Limit distribution; Statistics of sums; Matrix product ansatz; Hidden Markov model; Non-Gaussian distributions; FINITE-DIMENSIONAL REPRESENTATIONS; ASYMMETRIC EXCLUSION MODEL; ANOMALOUS DIFFUSION; QUADRATIC ALGEBRA; TIME-SERIES; STATES; FLUCTUATIONS;

D O I：

10.1007/s10955-014-1111-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to a form of ergodicity breaking in the underlying non-homogeneous Hidden Markov Chain. The link between ergodicity and limit distributions is detailed and used to provide a full algorithmic characterization of the general limit distributions.

引用

页码：1255 / 1283

页数：29

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