Generalized fractional Brownian motion /
This comprehensive book establishes the Zili generalized fractional Brownian motion (ZgfBm) as a powerful new foundation in the mathematical theory of stochastic processes. Generalized Fractional Brownian Motion provides the first rigorous and systematic stochastic analysis of the ZgfBm, a versatile...
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| Format: | eBook |
| Language: | English |
| Published: |
London, UK : Hoboken, NJ :
ISTE Ltd ; John Wiley & Sons, Inc.,
2026.
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| Series: | Mathematics and statistics series (ISTE)
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | This comprehensive book establishes the Zili generalized fractional Brownian motion (ZgfBm) as a powerful new foundation in the mathematical theory of stochastic processes. Generalized Fractional Brownian Motion provides the first rigorous and systematic stochastic analysis of the ZgfBm, a versatile Gaussian process that uniquely extends both the classic fractional Brownian motion with stationary increments and the sub-fractional Brownian motion with nonstationary increments. Defined by three tunable parameters, the ZgfBm offers unprecedented flexibility for modeling complex phenomena across diverse fields, overcoming the limitations of single-parameter models. The book carefully builds from foundational Gaussian theory and key fractional processes to advanced topics, including a complete methodology for parameter estimation, the development of a rigorous stochastic calculus with generalized It̥ formulas and an investigation into the regularity of solutions to stochastic heat equations. This essential resource provides researchers, practitioners and graduate students with a unified and in-depth perspective on advanced fractional Gaussian processes. |
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| Physical Description: | 1 online resource (xi, 233 pages) : color illustrations. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781394441549 1394441541 9781394441518 1394441517 9781394441532 1394441533 |