Yaozhong Hu Livres

The book delves into fractional Brownian motion (fBm), highlighting its applications across various fields such as biology and finance. It provides a thorough exploration of stochastic calculus for fBm, detailing various definitions of stochastic integration and their interconnections. While the content assumes a background in probability theory and stochastic analysis, essential mathematical concepts are revisited in the appendices. This resource serves as a crucial reference for graduate students and researchers in multiple disciplines, including mathematics, physics, and engineering.

The book explores the analysis of functions in finite-dimensional Euclidean spaces concerning the Lebesgue measure, highlighting its foundational role in mathematics. It addresses the complexities of extending these concepts to infinite dimensions, where the absence of Lebesgue measure presents challenges. The Gaussian measure emerges as the primary alternative in infinite-dimensional spaces, unified under the concept of "abstract Wiener space," providing a framework for understanding these advanced mathematical principles.

Focuses on combinatorial problems in mathematical competitions. This work provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces solutions to combinatorial problems and some typical problems with often-used solutions.