This book reflects upon the current trends arising in both the theoretical study and the practical modeling of phenomena that exhibit fractionality. There is a tendency to transition from one type of fractionality to several types presented simultaneously; thus, there is a need to construct models that include different types of fractionality. The authors of this book argue that one of the simplest approaches, suitable for applications in engineering, economics and finance, is the modeling of complex fractal properties using mixed models that are linear combinations of elementary fractional processes.
With this approach we can adequately model different levels of fractionality and not complicate the model too much. Based on these arguments, this book is devoted to mixed fractional Gaussian processes, that is, the linear combinations of fractional Brownian motions and sub-fractional Brownian motions. Beginning with a detailed description of the properties of separate fractional Gaussian components, this book will be useful both for beginners and for researchers and practitioners.
1. Gaussian Processes.
2. Fractional and Sub-fractional Brownian Motions.
3. Mixed Fractional and Mixed Sub-fractional Brownian Motions.
Yuliya Mishura is Full Professor and Head of the Department of Probability, Statistics and Actuarial Mathematics at Taras Shevchenko National University of Kyiv, Ukraine.
Mounir Zili is a Full Professor of Mathematics and member of the scientific council at the Faculty of Sciences of the University of Monastir, Tunisia.
Table of Contents
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