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Author: Paul Embrechts Publisher: Princeton University Press ISBN: 1400825105 Category : Mathematics Languages : en Pages : 125
Book Description
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: Paul Embrechts Publisher: Princeton University Press ISBN: 1400825105 Category : Mathematics Languages : en Pages : 125
Book Description
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: Ciprian Tudor Publisher: Springer Nature ISBN: 3031337727 Category : Mathematics Languages : en Pages : 110
Book Description
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.
Author: Oleg Sheluhin Publisher: John Wiley & Sons ISBN: 9780470062104 Category : Technology & Engineering Languages : en Pages : 334
Book Description
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: 3319009362 Category : Mathematics Languages : en Pages : 272
Book Description
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: 3319623311 Category : Mathematics Languages : en Pages : 143
Book Description
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: 9811251851 Category : Mathematics Languages : en Pages : 415
Book Description
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. Cataloging Policy and Support Office Publisher: ISBN: Category : Subject headings, Library of Congress Languages : en Pages : 1662
Author: Jan Beran Publisher: CRC Press ISBN: 9780412049019 Category : Mathematics Languages : en Pages : 336
Book Description
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.
Author: Paul Embrechts
Author: Paul Embrechts
Author: Ciprian Tudor
Author: Oleg Sheluhin
Author: Ciprian Tudor
Author: Vladas Pipiras
Author: Riccardo Gatto
Author: Library of Congress
Author: Library of Congress. Cataloging Policy and Support Office
Author: Pierre Patie
Author: Jan Beran