Mounir Zili, University of Monastir, Tunisia.
ISBN : 9781786309631
Publication Date : March 2026
Hardcover 256 pp
165.00 USD
Co-publisher
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 Itô 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.
1. Gaussian Processes.
2. Key Fractional Gaussian Processes: Building Blocks for the Generalized Fractional Brownian Motion.
3. The Zili Generalized Fractional Brownian Motion: Definition and Core Properties.
4. Parameter Estimation for the Generalized Fractional Brownian Motion.
5. Stochastic Calculus with Generalized Fractional Brownian Motion.
6. Stochastic Partial Differential Equations Driven by a ZgfBm Noise.
Mounir Zili is Full Professor of Mathematics and a key member of the “Analysis, Probability and Fractals” laboratory at the University of Monastir, Tunisia. He holds a PhD in Mathematics from Sorbonne University in Paris, France.
