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Non-Gaussian selfsimilar stochastic processes / Ciprian Tudor.

9783031337727 (electronic bk.)
3031337727 (electronic bk.)
9783031337710
3031337719

Cham : Springer, [2023]

©2023

English

1 online resource (xii, 101 pages).

10.1007/978-3-031-33772-7 doi

QA274.9

519.2/3

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.

Includes bibliographical references.

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Online resource; title from PDF title page (SpringerLink, viewed July 13, 2023).

Springer briefs in probability and mathematical statistics. 2365-4341

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