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

被引：0
|
作者：
Florian Angeletti
Eric Bertin
Patrice Abry
机构：
[1] National Institute for Theoretical Physics (NITheP),Institute of Theoretical Physics
[2] University of Stellenbosch,Laboratoire Interdisciplinaire de Physique, CNRS UMR 5588, BP 87
[3] Université Joseph Fourier Grenoble,Laboratoire de Physique, ENS Lyon, CNRS
[4] Université de Lyon,undefined
来源：
Journal of Statistical Physics | 2014年 / 157卷
关键词：
Limit distribution; Statistics of sums; Matrix product ansatz; Hidden Markov model; Non-Gaussian distributions;
D O I：
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中图分类号：
学科分类号：
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.
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页码：1255 / 1283
页数：28
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