Selfsimilar Processes

Author : Paul Embrechts
Publisher : Princeton University Press
ISBN 13 : 1400825105
Total Pages : 128 pages
Book Rating : 4.03/5 ( download)

DOWNLOAD NOW!

Download or read book Selfsimilar Processes written by Paul Embrechts and published by Princeton University Press. This book was released on 2009-01-10 with total page 128 pages. 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.

Author : Oleg Sheluhin
Publisher : John Wiley & Sons
ISBN 13 : 9780470062104
Total Pages : 334 pages
Book Rating : 4.0X/5 ( download)

DOWNLOAD NOW!

Download or read book Self-Similar Processes in Telecommunications written by Oleg Sheluhin and published by John Wiley & Sons. This book was released on 2007-03-13 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time the problems of voice services self-similarity are discussed systematically and in detail with specific examples and illustrations. Self-Similar Processes in Telecommunications considers the self-similar (fractal and multifractal) models of telecommunication traffic and efficiency based on the assumption that its traffic has fractal or multifractal properties (is self-similar). The theoretical aspects of the most well-known traffic models demonstrating self-similar properties are discussed in detail and the comparative analysis of the different models’ efficiency for self-similar traffic is presented. This book demonstrates how to use self-similar processes for designing new telecommunications systems and optimizing existing networks so as to achieve maximum efficiency and serviceability. The approach is rooted in theory, describing the algorithms (the logical arithmetical or computational procedures that define how a task is performed) for modeling these self-similar processes. However, the language and ideas are essentially accessible for those who have a general knowledge of the subject area and the advice is highly practical: all models, problems and solutions are illustrated throughout using numerous real-world examples. Adopts a detailed, theoretical, yet broad-based and practical mathematical approach for designing and operating numerous types of telecommunications systems and networks so as to achieve maximum efficiency Places the subject in context, describing the current algorithms that make up the fractal or self-similar processes while pointing to the future development of the technology Offers a comparative analysis of the different types of self-similar process usage within the context of local area networks, wide area networks and in the modeling of video traffic and mobile communications networks Describes how mathematical models are used as a basis for building numerous types of network, including voice, audio, data, video, multimedia services and IP (Internet Protocol) telephony The book will appeal to the wide range of specialists dealing with the design and exploitation of telecommunication systems. It will be useful for the post-graduate students, lecturers and researchers connected with communication networks disciplines.

Author : Ciprian Tudor
Publisher : Springer Science & Business Media
ISBN 13 : 3319009362
Total Pages : 272 pages
Book Rating : 4.60/5 ( download)

DOWNLOAD NOW!

Download or read book Analysis of Variations for Self-similar Processes written by Ciprian Tudor and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 272 pages. 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.

Author : Vladas Pipiras
Publisher : Springer
ISBN 13 : 3319623311
Total Pages : 143 pages
Book Rating : 4.13/5 ( download)

DOWNLOAD NOW!

Download or read book Stable Non-Gaussian Self-Similar Processes with Stationary Increments written by Vladas Pipiras and published by Springer. This book was released on 2017-08-31 with total page 143 pages. 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.

Author : Riccardo Gatto
Publisher : World Scientific
ISBN 13 : 9811251851
Total Pages : 415 pages
Book Rating : 4.56/5 ( download)

DOWNLOAD NOW!

Download or read book Stationary Stochastic Models: An Introduction written by Riccardo Gatto and published by World Scientific. This book was released on 2022-06-23 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a unified mathematical introduction to stationary time series models and to continuous time stationary stochastic processes. The analysis of these stationary models is carried out in time domain and in frequency domain. It begins with a practical discussion on stationarity, by which practical methods for obtaining stationary data are described. The presented topics are illustrated by numerous examples. Readers will find the following covered in a comprehensive manner:At the end, some selected topics such as stationary random fields, simulation of Gaussian stationary processes, time series for planar directions, large deviations approximations and results of information theory are presented. A detailed appendix containing complementary materials will assist the reader with many technical aspects of the book.

Author : Library of Congress
Publisher :
ISBN 13 :
Total Pages : 1160 pages
Book Rating : 4.40/5 ( download)

DOWNLOAD NOW!

Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2013 with total page 1160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Library of Congress. Cataloging Policy and Support Office
Publisher :
ISBN 13 :
Total Pages : 1662 pages
Book Rating : 4.66/5 ( download)

DOWNLOAD NOW!

Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2004 with total page 1662 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Pierre Patie
Publisher : American Mathematical Society
ISBN 13 : 1470449366
Total Pages : 182 pages
Book Rating : 4.60/5 ( download)

DOWNLOAD NOW!

Download or read book Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups written by Pierre Patie and published by American Mathematical Society. This book was released on 2021-11-16 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Author : Gennady Samoradnitsky
Publisher : Routledge
ISBN 13 : 1351414798
Total Pages : 519 pages
Book Rating : 4.91/5 ( download)

DOWNLOAD NOW!

Download or read book Stable Non-Gaussian Random Processes written by Gennady Samoradnitsky and published by Routledge. This book was released on 2017-11-22 with total page 519 pages. 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.

Author : Jan Beran
Publisher : CRC Press
ISBN 13 : 9780412049019
Total Pages : 336 pages
Book Rating : 4.15/5 ( download)

DOWNLOAD NOW!

Download or read book Statistics for Long-Memory Processes written by Jan Beran and published by CRC Press. This book was released on 1994-10-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Methods for Long Term Memory Processes covers the diverse statistical methods and applications for data with long-range dependence. Presenting material that previously appeared only in journals, the author provides a concise and effective overview of probabilistic foundations, statistical methods, and applications. The material emphasizes basic principles and practical applications and provides an integrated perspective of both theory and practice. This book explores data sets from a wide range of disciplines, such as hydrology, climatology, telecommunications engineering, and high-precision physical measurement. The data sets are conveniently compiled in the index, and this allows readers to view statistical approaches in a practical context. Statistical Methods for Long Term Memory Processes also supplies S-PLUS programs for the major methods discussed. This feature allows the practitioner to apply long memory processes in daily data analysis. For newcomers to the area, the first three chapters provide the basic knowledge necessary for understanding the remainder of the material. To promote selective reading, the author presents the chapters independently. Combining essential methodologies with real-life applications, this outstanding volume is and indispensable reference for statisticians and scientists who analyze data with long-range dependence.