This book offers an introduction to the field of stochastic analysis of Hermite processes.
These selfsimilar stochastic processes with stationary increments live in a Wiener chaos and
include the fractional Brownian motion the only Gaussian process in this class. Using the
Wiener chaos theory and multiple stochastic integrals the book covers the main properties of
Hermite processes and their multiparameter counterparts the Hermite sheets. It delves into the
probability distribution of these stochastic processes and their sample paths while also
presenting the basics of stochastic integration theory with respect to Hermite processes and
sheets.The book goes beyond theory and provides a thorough analysis of physical models driven
by Hermite noise including the Hermite Ornstein-Uhlenbeck process and the solution to the
stochastic heat equation driven by such a random perturbation. Moreover it explores up-to-date
topics central to current research in statistical inference for Hermite-driven models.
