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Stochastic Analysis of Mixed Fractional Gaussian Processes presents the main tools necessary to characterize Gaussian processes. The book focuses on the particular case of the linear combination of independent fractional and sub-fractional Brownian motions with different Hurst indices. Stochastic integration with respect to these processes is considered, as is the study of the existence and uniqueness of solutions of related SDE's. Applications in finance and statistics are also explored, with each chapter supplying a number of exercises to illustrate key concepts.
- Presents both mixed fractional and sub-fractional Brownian motions
- Provides an accessible description for mixed fractional gaussian processes that is ideal for Master's and PhD students
- Includes different Hurst indices
Master's and Phd students and researchers specializing in statistics, stochastics and finances
1. Gaussian Processes
2. Fractional and Sub-fractional Brownian Motions
3. Mixed Fractional and Mixed Sub-fractional Brownian Motions
- No. of pages:
- © ISTE Press - Elsevier 2018
- 22nd May 2018
- ISTE Press - Elsevier
- Hardcover ISBN:
- eBook ISBN:
Yuliya Mishura is Professor and Head of the Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Ukraine. Her research interests include stochastic analysis, theory of stochastic processes, stochastic differential equations, numerical schemes, financial mathematics, risk processes, statistics of stochastic processes, and models with long-range dependence.
Head, Department of Probability, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko Kyiv National University, Kiev, Ukraine
Mounir Zili works at the University of Monastir, Faculty of sciences of Monastir with expertise in Probability Theory, Applied Mathematics, Analysis
Professor, Faculty of Sciences, Monastir-University of Monastir
"The book under review deals with two classes of specific Gaussian processes, namely, (mixed) fractional Brownian motion and (mixed) sub fractional Brownian motion." --Mathematical Reviews Clippings
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