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.
引用
收藏
页数:21
相关论文
共 50 条
  • [1] STATIONARY OPERATOR FOR NON-STATIONARY PROCESSES
    ZUBAREV, DN
    DOKLADY AKADEMII NAUK SSSR, 1965, 164 (03): : 537 - &
  • [2] Multifractal analysis of a class of additive processes with correlated non-stationary increments
    Barral, J
    Wéhel, JL
    ELECTRONIC JOURNAL OF PROBABILITY, 2004, 9 : 508 - 543
  • [3] Hausdorff Measure of Space Anisotropic Gaussian Processes with Non-stationary Increments
    Wang, Jun
    Chen, Zhen-long
    Yuan, Wei-jie
    Shen, Guang-jun
    ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2025, 41 (01): : 114 - 132
  • [4] Hausdorff Measure of Space Anisotropic Gaussian Processes with Non-stationary Increments
    Jun WANG
    Zhenlong CHEN
    Weijie YUAN
    Guangjun SHEN
    Acta Mathematicae Applicatae Sinica, 2025, 41 (01) : 114 - 132
  • [5] Surveillance of non-stationary processes
    Lazariv, Taras
    Schmid, Wolfgang
    ASTA-ADVANCES IN STATISTICAL ANALYSIS, 2019, 103 (03) : 305 - 331
  • [6] NON-STATIONARY PROCESSES AND SPECTRUM
    NAGABHUSHANAM, K
    BHAGAVAN, CS
    CANADIAN JOURNAL OF MATHEMATICS, 1968, 20 (05): : 1203 - +
  • [7] ON PREDICTION OF NON-STATIONARY PROCESSES
    ABDRABBO, NA
    PRIESTLE.MB
    JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 1967, 29 (03) : 570 - &
  • [8] Predicting non-stationary processes
    Ryabko, Daniil
    Hutter, Marcus
    APPLIED MATHEMATICS LETTERS, 2008, 21 (05) : 477 - 482
  • [9] Surveillance of non-stationary processes
    Taras Lazariv
    Wolfgang Schmid
    AStA Advances in Statistical Analysis, 2019, 103 : 305 - 331
  • [10] Riemann Integral Operator for Stationary and Non-Stationary Processes
    Alexandrovich, I. M.
    Lyashko, S. I.
    Sydorov, M. V. -S.
    Lyashko, N. I.
    Bondar, O. S.
    CYBERNETICS AND SYSTEMS ANALYSIS, 2021, 57 (06) : 918 - 926