A consistent estimator of the entropy of measures and dynamical systems

被引：2
|
作者：
Timofeev, EA [1 ]
机构：
[1] Yaroslavl State Univ, Yaroslavl, Russia
来源：
MATHEMATICAL NOTES | 2005年 / 77卷 / 5-6期
关键词：
entropy; statistical estimator; Hausdorff dimension; dynamical system; ergodicity;
D O I：
10.1007/s11006-005-0083-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An the paper, a new invariant of measures and dynamical systems, called statentropy, is described. A statistical estimator for statentropy, computed without using auxiliary estimates of measures, is constructed. It is proved that the proposed statistical estimator is consistent under fairly general restrictions. We show that for exact dimensional measures, statentropy coincides with the Hausdorff dimension of the measure, and for ergodic dynamical systems, it coincides with the metric entropy of the map.
引用
收藏
页码：831 / 842
页数：12
相关论文
共 50 条
  • [41] Logical entropy of dynamical systems in product MV-algebras and general scheme
    Markechova, Dagmar
    Riecan, Beloslav
    ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (1)
  • [42] The entropy of semi-independent hyper MV-algebra dynamical systems
    Mehrpooya, Adel
    Ebrahimi, Mohammad
    Davvaz, Bijan
    SOFT COMPUTING, 2016, 20 (04) : 1263 - 1276
  • [43] Logical entropy of dynamical systems in product MV-algebras and general scheme
    Dagmar Markechová
    Beloslav Riečan
    Advances in Difference Equations, 2019
  • [44] The entropy of semi-independent hyper MV-algebra dynamical systems
    Adel Mehrpooya
    Mohammad Ebrahimi
    Bijan Davvaz
    Soft Computing, 2016, 20 : 1263 - 1276
  • [45] The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
    Giordano, C. M.
    Cincotta, P. M.
    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2018, 130 (05):
  • [46] A NEW ESTIMATOR OF ENTROPY
    CORREA, JC
    COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1995, 24 (10) : 2439 - 2449
  • [47] An operator theoretical approach to the sequence entropy of dynamical systems
    Rahimi, M.
    Anjedani, M. Mohammadi
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2022, 37 (01): : 56 - 65
  • [48] ENTROPY OF MV-ALGEBRAIC DYNAMICAL SYSTEMS: AN EXAMPLE
    Barbieri, Giuseppina
    Lenzi, Giacomo
    MATHEMATICA SLOVACA, 2019, 69 (02) : 267 - 274
  • [49] The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
    C. M. Giordano
    P. M. Cincotta
    Celestial Mechanics and Dynamical Astronomy, 2018, 130
  • [50] The entropy of fuzzy dynamical systems, general scheme and generators
    Riecan, B
    Markechova, D
    FUZZY SETS AND SYSTEMS, 1998, 96 (02) : 191 - 199
12345