高斯分布各种熵的性质及分数阶过程熵的比较

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED Axioms Pub Date : 2023-10-31 DOI:10.3390/axioms12111026

Anatoliy Malyarenko, Yuliya Mishura, Kostiantyn Ralchenko, Yevheniia Anastasiia Rudyk

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引用次数: 0

摘要

本文考虑了五种高斯分布熵:Shannon熵、r尼米特熵、广义r尼米特熵、Tsallis熵和Sharma-Mittal熵，建立了它们之间的相互关系和它们作为参数函数的性质。然后，我们考虑分数阶高斯过程，即分数阶、次分数阶、双分数阶、多分数阶和回火分数阶布朗运动，并比较这些过程的一维分布的熵。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Properties of Various Entropies of Gaussian Distribution and Comparison of Entropies of Fractional Processes

We consider five types of entropies for Gaussian distribution: Shannon, Rényi, generalized Rényi, Tsallis and Sharma–Mittal entropy, establishing their interrelations and their properties as the functions of parameters. Then, we consider fractional Gaussian processes, namely fractional, subfractional, bifractional, multifractional and tempered fractional Brownian motions, and compare the entropies of one-dimensional distributions of these processes.

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来源期刊

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.