Non-Gaussian Selfsimilar Stochastic Processes
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Beschreibung
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 researchin statistical inference for Hermite-driven models.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.Presents the main elements of Wiener chaos and multiple stochastic integrals Provides a framework for stochastic integration theory with respect to Hermite processes Discusses statistical inference with Hermite perturbation
Autor*in
Ciprian Tudor
Themen in »Non-Gaussian Selfsimilar Stochastic Processes«
Non-Gaussian Stochastic Processes Hermite Processes Stochastic Integration of Hermite Processes Selfsimilar Stochastic Processes Wiener chaos Mulitple Stochastic Integrals Stochastic Differential Equations Parameter Estimation Hermite noise
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“The book is written in a clear and self-contained manner, thanks to the expertise of the author in related topics, and could serve as a nice self-studying reference for graduate students.” (Yizao Wang, Mathematical Reviews, December, 2024)
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