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.
General
| Imprint: |
Springer International Publishing AG
|
| Country of origin: |
Switzerland |
| Series: |
SpringerBriefs in Probability and Mathematical Statistics |
| Release date: |
July 2023 |
| First published: |
2023 |
| Authors: |
Ciprian Tudor
|
| Dimensions: |
235 x 155mm (L x W) |
| Pages: |
101 |
| Edition: |
1st ed. 2023 |
| ISBN-13: |
978-3-03-133771-0 |
| Categories: |
Books
|
| LSN: |
3-03-133771-9 |
| Barcode: |
9783031337710 |
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