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Author: Vladas Pipiras
Publisher: Cambridge University Press
Published: 2017-04-18
Total Pages: 693
ISBN-13: 1107039460
DOWNLOAD EBOOKA modern and rigorous introduction to long-range dependence and self-similarity, complemented by numerous more specialized up-to-date topics in this research area.
Author: Gennady Samorodnitsky
Publisher: Springer
Published: 2016-11-09
Total Pages: 419
ISBN-13: 3319455753
DOWNLOAD EBOOKThis monograph is a gateway for researchers and graduate students to explore the profound, yet subtle, world of long-range dependence (also known as long memory). The text is organized around the probabilistic properties of stationary processes that are important for determining the presence or absence of long memory. The first few chapters serve as an overview of the general theory of stochastic processes which gives the reader sufficient background, language, and models for the subsequent discussion of long memory. The later chapters devoted to long memory begin with an introduction to the subject along with a brief history of its development, followed by a presentation of what is currently the best known approach, applicable to stationary processes with a finite second moment. The book concludes with a chapter devoted to the author’s own, less standard, point of view of long memory as a phase transition, and even includes some novel results. Most of the material in the book has not previously been published in a single self-contained volume, and can be used for a one- or two-semester graduate topics course. It is complete with helpful exercises and an appendix which describes a number of notions and results belonging to the topics used frequently throughout the book, such as topological groups and an overview of the Karamata theorems on regularly varying functions.
Author: Paul Doukhan
Publisher: Springer Science & Business Media
Published: 2002-12-13
Total Pages: 744
ISBN-13: 9780817641689
DOWNLOAD EBOOKThe area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become quite simplified and has greatly affected such areas as finance and telecommunications. Even non-specialists try to analyze data sets and ask basic questions about their structure. One such question is whether one observes some type of invariance with respect to scale, a question that is closely related to the existence of long-range dependence in the data. This important topic of long-range dependence is the focus of this unique work, written by a number of specialists on the subject. The topics selected should give a good overview from the probabilistic and statistical perspective. Included will be articles on fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, and prediction for long-range dependence sequences. For those graduate students and researchers who want to use the methodology and need to know the "tricks of the trade," there will be a special section called "Mathematical Techniques." Topics in the first part of the book are covered from probabilistic and statistical perspectives and include fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, prediction for long-range dependence sequences. The reader is referred to more detailed proofs if already found in the literature. The last part of the book is devoted to applications in the areas of simulation, estimation and wavelet techniques, traffic in computer networks, econometry and finance, multifractal models, and hydrology. Diagrams and illustrations enhance the presentation. Each article begins with introductory background material and is accessible to mathematicians, a variety of practitioners, and graduate students. The work serves as a state-of-the art reference or graduate seminar text.
Author: Jan Beran
Publisher: Springer Science & Business Media
Published: 2013-05-14
Total Pages: 892
ISBN-13: 3642355129
DOWNLOAD EBOOKLong-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant.
Author: Ming Li
Publisher: Frontiers Media SA
Published: 2022-12-05
Total Pages: 160
ISBN-13: 2832508502
DOWNLOAD EBOOKAuthor: Jacques Lévy-Véhel
Publisher: Springer Science & Business Media
Published: 2005-12-06
Total Pages: 288
ISBN-13: 1846280486
DOWNLOAD EBOOKThe application of fractals in the engineering sciences is evolving swiftly and the editors have turned to Springer for the third time to bring you the latest research emerging from the rapid growth in techniques available for the employment of the ideas of fractals and complexity to a variety of disciplines in and associated with the engineering field. The strong potential of this research can be seen in real industrial situations with recent progress being made in areas such as chemical engineering, internet traffic, physics and finance. Image processing continues to be a major field of application for fractal analysis and is well-represented here. It is important to note that the applications models are presented with a firm basis in theoretical argument, the qualitative observation of fractal phenomena no longer being sufficient. Consisting of papers written by a world-wide pool of experts, the multidisciplinary approach of this third volume will be of particular interest to industrial researchers and practitioners as well as to academics from many backgrounds. Fractals in Engineering: New Trends in Theory and Applications continues the publication of engineering-related research in fractal techniques begun in Fractals in Engineering and Fractals: Theory and Applications in Engineering (Springer London 1997 and 1999).
Author: Piotr Gaj
Publisher: Springer
Published: 2015-05-27
Total Pages: 471
ISBN-13: 3319194194
DOWNLOAD EBOOKThis book constitutes the thoroughly refereed proceedings of the 22st International Conference on Computer Networks, CN 2015, held in Brunów, Poland, in June 2015. The 42 revised full papers presented were carefully reviewed and selected from 79 submissions. The papers in these proceedings cover the following topics: computer networks, distributed computer systems, communications and teleinformatics.
Author: Oleg Sheluhin
Publisher: John Wiley & Sons
Published: 2007-03-13
Total Pages: 334
ISBN-13: 9780470062104
DOWNLOAD EBOOKFor 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: Gilles Teyssière
Publisher: Springer Science & Business Media
Published: 2006-09-22
Total Pages: 394
ISBN-13: 3540346252
DOWNLOAD EBOOKAssembles three different strands of long memory analysis: statistical literature on the properties of, and tests for, LRD processes; mathematical literature on the stochastic processes involved; and models from economic theory providing plausible micro foundations for the occurrence of long memory in economics.
Author: Ming Li
Publisher: CRC Press
Published: 2022-12-29
Total Pages: 297
ISBN-13: 100081789X
DOWNLOAD EBOOKThis book provides a comprehensive theory of mono- and multi-fractal traffic, including the basics of long-range dependent time series and 1/f noise, ergodicity and predictability of traffic, traffic modeling and simulation, stationarity tests of traffic, traffic measurement and the anomaly detection of traffic in communications networks. Proving that mono-fractal LRD time series is ergodic, the book exhibits that LRD traffic is stationary. The author shows that the stationarity of multi-fractal traffic relies on observation time scales, and proposes multi-fractional generalized Cauchy processes and modified multi-fractional Gaussian noise. The book also establishes a set of guidelines for determining the record length of traffic in measurement. Moreover, it presents an approach of traffic simulation, as well as the anomaly detection of traffic under distributed-denial-of service attacks. Scholars and graduates studying network traffic in computer science will find the book beneficial.
