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

Author

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

Subjects
Shannon entropy, Rényi entropy, Tsallis entropy, Sharma–Mittal entropy, normal distribution, fractional Brownian motion, Mathematics, QA1-939
Abstract

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.

Published
2023
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