Information Theory for Non-Stationary Processes with Stationary Increments

被引:14
|
作者
Granero-Belinchon, Carlos [1 ,2 ]
Roux, Stephane G. [1 ]
Garnier, Nicolas B. [1 ]
机构
[1] Univ Claude Bernard, Ens Lyon, Univ Lyon, CNRS,Lab Phys, F-69342 Lyon, France
[2] Univ Toulouse, ONERA DOTA, FR-31055 Toulouse, France
关键词
entropy; entropy rate; non-stationary; scale invariance; non-Gaussian; SELF-SIMILARITY; TURBULENCE; ENSEMBLE; MOTIONS;
D O I
10.3390/e21121223
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We describe how to analyze the wide class of non-stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability distributions. These ersatz versions of entropy, mutual information, and entropy rate can be estimated when only a single realization of the process is available. We abundantly illustrate our approach by analyzing Gaussian and non-Gaussian self-similar signals, as well as multi-fractal signals. Using Gaussian signals allows us to check that our approach is robust in the sense that all quantities behave as expected from analytical derivations. Using the stationarity (independence on the integration time) of the ersatz entropy rate, we show that this quantity is not only able to fine probe the self-similarity of the process, but also offers a new way to quantify the multi-fractality.
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页数:21
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