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Non-Gaussian Selfsimilar Stochastic Processes

2023
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Release : 2023
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Kind : eBook
Book Rating : 734/5 ( reviews)

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Book Synopsis Non-Gaussian Selfsimilar Stochastic Processes by : Ciprian Tudor

Download or read book Non-Gaussian Selfsimilar Stochastic Processes written by Ciprian Tudor. This book was released on 2023. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stable Non-Gaussian Self-Similar Processes with Stationary Increments

2017-08-31 Mathematics
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Release : 2017-08-31
Genre : Mathematics
Kind : eBook
Book Rating : 311/5 ( reviews)

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Book Synopsis Stable Non-Gaussian Self-Similar Processes with Stationary Increments by : Vladas Pipiras

Download or read book Stable Non-Gaussian Self-Similar Processes with Stationary Increments written by Vladas Pipiras. This book was released on 2017-08-31. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called deterministic flows. The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity. In-depth appendices are also included. This book is aimed at graduate students and researchers working in probability theory and statistics.

Non-Gaussian Selfsimilar Stochastic Processes

2023-07-04 Mathematics
Download Non-Gaussian Selfsimilar Stochastic Processes PDF Online Free

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Release : 2023-07-04
Genre : Mathematics
Kind : eBook
Book Rating : 727/5 ( reviews)

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Book Synopsis Non-Gaussian Selfsimilar Stochastic Processes by : Ciprian Tudor

Download or read book Non-Gaussian Selfsimilar Stochastic Processes written by Ciprian Tudor. This book was released on 2023-07-04. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stable Non-Gaussian Random Processes

2017-11-22 Mathematics
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Release : 2017-11-22
Genre : Mathematics
Kind : eBook
Book Rating : 798/5 ( reviews)

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Book Synopsis Stable Non-Gaussian Random Processes by : Gennady Samoradnitsky

Download or read book Stable Non-Gaussian Random Processes written by Gennady Samoradnitsky. This book was released on 2017-11-22. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.

Selfsimilar Processes

2009-01-10 Mathematics
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Release : 2009-01-10
Genre : Mathematics
Kind : eBook
Book Rating : 105/5 ( reviews)

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Book Synopsis Selfsimilar Processes by : Paul Embrechts

Download or read book Selfsimilar Processes written by Paul Embrechts. This book was released on 2009-01-10. Available in PDF, EPUB and Kindle. Book excerpt: The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.

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