Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index

被引：2

作者：

Malyarenko, Anatoliy ^{[1
]}

Mishura, Yuliya ^{[1
,2
]}

Ralchenko, Kostiantyn ^{[2
]}

Shklyar, Sergiy ^{[2
]}

机构：

[1] Malardalen Univ, Div Math & Phys, S-72123 Vasteras, Sweden

[2] Taras Shevchenko Natl Univ Kyiv, Dept Probabil Theory Stat & Actuarial Math, 64-13,Volodymyrska St, UA-01601 Kiev, Ukraine

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2023年 / 26卷 / 03期

基金：

日本科学技术振兴机构;

关键词：

Fractional Gaussian noise; Hurst index; Entropy; Entropy functionals; Entropy rate; BROWNIAN-MOTION; PERMUTATION ENTROPY; CALCULUS; COMPLEXITY; RESPECT;

D O I：

10.1007/s13540-023-00155-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the study of the properties of entropy as a function of the Hurst index, which corresponds to the fractional Gaussian noise. Since the entropy of the Gaussian vector depends on the determinant of the covariance matrix, and the behavior of this determinant as a function of the Hurst index is rather difficult to study analytically at high dimensions, we also consider simple alternative entropy functionals, whose behavior, on the one hand, mimics the behavior of entropy and, on the other hand, is not difficult to study. Asymptotic behavior of the normalized entropy (so called entropy rate) is also studied for the entropy and for the alternative functionals.

引用

页码：1052 / 1081

页数：30

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