Yuliya Mishura, Kostiantyn Ralchenko

Entropies and Fractionality

Entropy Functionals, Small Deviations and Related Integral Equations

• Gebundenes Buch

Produktbeschreibung

Entropies and Fractionality: Entropy Functionals, Small Deviations and Related Integral Equations starts with a systematization and calculation of various entropies (Shannon, Rényi and some others) of selected absolutely continuous probability distributions.

Produktdetails

• Verlag: Chapman and Hall/CRC
• Seitenzahl: 274
• Erscheinungstermin: 20. Oktober 2025
• Englisch
• Abmessung: 240mm x 161mm x 19mm
• Gewicht: 578g
• ISBN-13: 9781041074786
• ISBN-10: 1041074786
• Artikelnr.: 73871589

Autorenporträt

Yuliya Mishura received her PhD in probability and statistics in Kyiv University in 1978 and completed her postdoctoral degree in probability and statistics (Habilitation) in 1990. She is currently a Professor of the Department of Probability, Statistics and Actuarial Mathematics at Taras Shevchenko National University of Kyiv. Having broad and varied scientific interests, she is the author/coauthor of more than 320 research papers and more than 20 books. Her research interests include theory and statistics of stochastic processes, stochastic differential equations, fractional calculus and fractional processes, stochastic analysis, functional limit theorems, entropies of probability distributions and stochastic systems, financial mathematics and other applications of stochastics. Invited speaker of many international congresses and conferences, organizer of series of conferences. Editor- in-chief of the journal "Theory of Probability and Mathematical Statistics", coeditor-in-chief of the journal "Modern Stochastics: Theory and Applications". Team leader and participant of many international research projects. Kostiantyn Ralchenko obtained his PhD in Probability and Statistics from Taras Shevchenko National University of Kyiv in 2012 and completed his postdoctoral qualification (Habilitation) in the same field in 2019. He currently holds the position of Professor in the Department of Probability, Statistics, and Actuarial Mathematics at Taras Shevchenko National University of Kyiv. He is the author/co-author of more than 60 research papers and 4 scientific monographs. His research interests include the theory and statistical analysis of stochastic processes, fractional and multifractional processes, ordinary and partial stochastic differential equations, entropy measures of probability distributions and stochastic systems, as well as financial mathematics.

Inhaltsangabe

Preface
Introduction
I Entropies and Entropy Risk Measures Related to Probability Distributions
1 Entropies of Selected Distributions and Their Properties
2 Entropic Risk Measure EVaR in Relation to Selected Distributions
II Entropies and Entropy Functionals Related to Fractional Stochastic
Processes
3 Entropies of Fractional Processes
4 Fractional Gaussian Noise: Entropy, Entropy Rate and Alternative Entropy
Functionals
5 Evaluation of Extreme Values of the Relative Entropy Functionals Related
to the Mixture of Wiener Processes
6 Entropy Optimization for a Mixture of Standard and Fractional Brownian
Motions
III Small Deviations of the Mixed Fractional Processes and Numerical
Solution of the Related Integral Equations
7 Optimization of Small Deviation for Mixed Fractional Brownian Motion with
Trend
8 Approximate Solution of the Integral Equations Involving Kernel with
Additional Singularity
A Elements of Calculus, Fractional Calculus and Stochastics
Bibliography
Index