Non-Gaussian Selfsimilar Stochastic Processes

• Verfasst von: Tudor, Ciprian [VerfasserIn]
• Titel: Non-Gaussian Selfsimilar Stochastic Processes
• Verf.angabe: by Ciprian Tudor
• Ausgabe: 1st ed. 2023.
• Verlagsort: Cham
• Verlagsort: Cham
• Verlag: Springer Nature Switzerland
• Verlag: Imprint: Springer
• E-Jahr: 2023
• Jahr: 2023.
• Jahr: 2023.
• Umfang: 1 Online-Ressource(XII, 101 p. 1 illus.)
• Gesamttitel/Reihe: SpringerBriefs in Probability and Mathematical Statistics
• ISBN: 978-3-031-33772-7
• DOI: doi:10.1007/978-3-031-33772-7
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• K10plus-PPN: 1852345616
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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.

Abstract

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.