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Analysis of Variations for Self-similar Processes

2013-08-13 Mathematics
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Release : 2013-08-13
Genre : Mathematics
Kind : eBook
Book Rating : 362/5 ( reviews)

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Book Synopsis Analysis of Variations for Self-similar Processes by : Ciprian Tudor

Download or read book Analysis of Variations for Self-similar Processes written by Ciprian Tudor. This book was released on 2013-08-13. Available in PDF, EPUB and Kindle. Book excerpt: Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.

Analysis of Variations for Self-similar Processes

2013-08-08 Mathematics
Download Analysis of Variations for Self-similar Processes PDF Online Free

Author :
Release : 2013-08-08
Genre : Mathematics
Kind : eBook
Book Rating : 377/5 ( reviews)

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Book Synopsis Analysis of Variations for Self-similar Processes by : Ciprian A. Tudor

Download or read book Analysis of Variations for Self-similar Processes written by Ciprian A. Tudor. This book was released on 2013-08-08. Available in PDF, EPUB and Kindle. Book excerpt: Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.

Non-Gaussian Selfsimilar Stochastic Processes

2023-07-04 Mathematics
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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.

Stochastic Analysis and Related Topics

2017-10-04 Mathematics
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Release : 2017-10-04
Genre : Mathematics
Kind : eBook
Book Rating : 713/5 ( reviews)

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Book Synopsis Stochastic Analysis and Related Topics by : Fabrice Baudoin

Download or read book Stochastic Analysis and Related Topics written by Fabrice Baudoin. This book was released on 2017-10-04. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this collection are a sampling of some of the research presented during the conference “Stochastic Analysis and Related Topics”, held in May of 2015 at Purdue University in honor of the 60th birthday of Rodrigo Bañuelos. A wide variety of topics in probability theory is covered in these proceedings, including heat kernel estimates, Malliavin calculus, rough paths differential equations, Lévy processes, Brownian motion on manifolds, and spin glasses, among other topics.

Long-Range Dependence and Self-Similarity

2017-04-18 Business & Economics
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Release : 2017-04-18
Genre : Business & Economics
Kind : eBook
Book Rating : 460/5 ( reviews)

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Book Synopsis Long-Range Dependence and Self-Similarity by : Vladas Pipiras

Download or read book Long-Range Dependence and Self-Similarity written by Vladas Pipiras. This book was released on 2017-04-18. Available in PDF, EPUB and Kindle. Book excerpt: A modern and rigorous introduction to long-range dependence and self-similarity, complemented by numerous more specialized up-to-date topics in this research area.

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