Non-Gaussian selfsimilar stochastic processes / Ciprian Tudor.
Tudor, Ciprian, 1973- author.
2023
QA274.9
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Title
Non-Gaussian selfsimilar stochastic processes / Ciprian Tudor.
Author
Tudor, Ciprian, 1973- author.
ISBN
9783031337727 (electronic bk.)
3031337727 (electronic bk.)
9783031337710
3031337719
DOI
https://doi.org/10.1007/978-3-031-33772-7
Published
Cham : Springer, [2023]
Copyright
©2023
Language
English
Description
1 online resource (xii, 101 pages).
Item Number
10.1007/978-3-031-33772-7 doi
Call Number
QA274.9
Dewey Decimal Classification
519.2/3
Summary
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.
Bibliography, etc. Note
Includes bibliographical references.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 13, 2023).
Series
Springer briefs in probability and mathematical statistics. 2365-4341
Available in Other Form
Non-Gaussian Selfsimilar Stochastic Processes
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Introduction
Chapter 1. Multiple Stochastic Integrals
Chapter 2. Hermite processes: Definition and basic properties
Chapter 3. The Wiener integral with respect to the Hermite process and the Hermite Ornstein-Uhlenbeck process
Chapter 4. Hermite sheets and SPDEs
Chapter 5. Statistical inference for stochastic (partial) differential equations with Hermite noise
References.

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