Introduction

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.

Parameters and Flexibility

Defined by three tunable parameters, the ZgfBm offers unprecedented flexibility for modeling complex phenomena across diverse fields, overcoming the limitations of single-parameter models.

Content and Topics

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.

Audience and Purpose

This essential resource provides researchers, practitioners, and graduate students with a unified and in-depth perspective on advanced fractional Gaussian processes.