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, subfractiona...

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Bibliographic Details
Published in:	Axioms Vol. 12; no. 11; p. 1026
Main Authors:	Malyarenko, Anatoliy, Mishura, Yuliya, Ralchenko, Kostiantyn, Rudyk, Yevheniia Anastasiia
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01-10-2023
Subjects:	Analysis Brownian motion Critical phenomena Data compression Entropy fractional Brownian motion Gaussian process Gaussian processes Hypotheses Information theory Investigations matematik/tillämpad matematik Mathematics/Applied Mathematics Normal distribution Phase transitions Physics Probability distribution Random variables Rényi entropy Shannon entropy Sharma–Mittal entropy Signal processing Statistical mechanics Tsallis entropy Rényi entropy Tsallis entropy Sharma–Mittal entropy bifractional Brownian motion multifractional Brownian motion Shannon entropy normal distribution fractional Brownian motion tempered fractional Brownian motion subfractional Brownian motion
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Summary:	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.
ISSN:	2075-1680 2075-1680
DOI:	10.3390/axioms12111026