Analysis Of Variations For Self Similar Processes

Author : Ciprian Tudor
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 47,5 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9783319009360

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Analysis of Variations for Self-similar Processes by Ciprian Tudor Pdf

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 : Ciprian A. Tudor
Publisher : Springer
Page : 268 pages
File Size : 40,7 Mb
Release : 2013-08-08
Category : Mathematics
ISBN : 3319009370

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Analysis of Variations for Self-similar Processes by Ciprian A. Tudor Pdf

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 : Fabrice Baudoin,Jonathon Peterson
Publisher : Birkhäuser
Page : 221 pages
File Size : 49,5 Mb
Release : 2017-10-04
Category : Mathematics
ISBN : 9783319596716

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Stochastic Analysis and Related Topics by Fabrice Baudoin,Jonathon Peterson Pdf

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.

Author : Vladas Pipiras,Murad S. Taqqu
Publisher : Cambridge University Press
Page : 693 pages
File Size : 42,5 Mb
Release : 2017-04-18
Category : Business & Economics
ISBN : 9781107039469

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Long-Range Dependence and Self-Similarity by Vladas Pipiras,Murad S. Taqqu Pdf

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.

Author : Ciprian Tudor
Publisher : Springer Nature
Page : 110 pages
File Size : 53,8 Mb
Release : 2023-07-04
Category : Mathematics
ISBN : 9783031337727

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Non-Gaussian Selfsimilar Stochastic Processes by Ciprian Tudor Pdf

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 : Jaya P. N. Bishwal
Publisher : Springer Nature
Page : 634 pages
File Size : 55,5 Mb
Release : 2022-08-06
Category : Mathematics
ISBN : 9783031038617

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Parameter Estimation in Stochastic Volatility Models by Jaya P. N. Bishwal Pdf

This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Author : Paul Embrechts
Publisher : Princeton University Press
Page : 128 pages
File Size : 53,6 Mb
Release : 2009-01-10
Category : Mathematics
ISBN : 9781400825103

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Selfsimilar Processes by Paul Embrechts Pdf

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 : Yves Meyer,Sylvie Roques
Publisher : Atlantica Séguier Frontières
Page : 808 pages
File Size : 46,5 Mb
Release : 1993
Category : Wavelets
ISBN : 2863321307

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Progress in Wavelet Analysis and Applications by Yves Meyer,Sylvie Roques Pdf

Author : Sergey Balandin,Yevgeni Koucheryavy,Honglin Hu
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 50,8 Mb
Release : 2011-07-28
Category : Computers
ISBN : 9783642228742

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Smart Spaces and Next Generation Wired/Wireless Networking by Sergey Balandin,Yevgeni Koucheryavy,Honglin Hu Pdf

This book constitutes the refereed proceedings of the 11th International Conference on Next Generation Teletraffic and Wired/Wireless Advanced Networking, NEW2AN 2011 and the 4th Conference on Smart Spaces, ruSMART 2011 jointly held in St. Petersburg, Russia, in August 2011. The 56 revised full papers presented were carefully reviewed and selected from numerous submissions. The ruSMART papers are organized in topical sections on role of context in smart spaces, smart spaces platforms and smart-M3, methods for studying smart spaces, and smart spaces solutions. The NEW2AN papers are organized in topical sections on wireless PHY and power control, ad hoc networks, WSN, special topics, simulation + fundamental analysis I, traffic modeling and measurement, simulation + fundamental analysis II, network performance and QoS, cooperative, P2P, overlay networks and content, applications and services, API and software, and video.

Author : Govindan Rangarajan,Mingzhou Ding
Publisher : Springer
Page : 406 pages
File Size : 44,7 Mb
Release : 2008-01-11
Category : Medical
ISBN : 9783540448327

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Processes with Long-Range Correlations by Govindan Rangarajan,Mingzhou Ding Pdf

Processes with long range correlations occur in a wide variety of fields ranging from physics and biology to economics and finance. This book, suitable for both graduate students and specialists, brings the reader up to date on this rapidly developing field. A distinguished group of experts have been brought together to provide a comprehensive and well-balanced account of basic notions and recent developments. The book is divided into two parts. The first part deals with theoretical developments in the area. The second part comprises chapters dealing primarily with three major areas of application: anomalous diffusion, economics and finance, and biology (especially neuroscience).

Author : Vladas Pipiras,Murad S. Taqqu
Publisher : Springer
Page : 135 pages
File Size : 48,5 Mb
Release : 2017-08-31
Category : Mathematics
ISBN : 9783319623313

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Stable Non-Gaussian Self-Similar Processes with Stationary Increments by Vladas Pipiras,Murad S. Taqqu Pdf

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 : Oleg Sheluhin,Sergey Smolskiy,Andrew Osin
Publisher : John Wiley & Sons
Page : 334 pages
File Size : 48,7 Mb
Release : 2007-03-13
Category : Technology & Engineering
ISBN : 047006210X

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Self-Similar Processes in Telecommunications by Oleg Sheluhin,Sergey Smolskiy,Andrew Osin Pdf

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 : Ming Li,Carlo Cattani
Publisher : Frontiers Media SA
Page : 160 pages
File Size : 53,9 Mb
Release : 2022-12-05
Category : Science
ISBN : 9782832508503

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Long-Range Dependent Processes: Theory and Applications by Ming Li,Carlo Cattani Pdf

Author : Jarmo Harju
Publisher : Springer Science & Business Media
Page : 597 pages
File Size : 40,9 Mb
Release : 2006-05-15
Category : Computers
ISBN : 9783540344292

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Next Generation Teletraffic and Wired/Wireless Advanced Networking by Jarmo Harju Pdf

This book constitutes the refereed proceedings of the 6th International Conference on Next Generation Teletraffic and Wired/Wireless Advanced Networking, NEW2AN 2006, held in St. Petersburg, Russia in May/June 2006. The 49 revised full papers presented together with 2 keynote talks were carefully reviewed and selected from a total of 137 submissions. The papers are organized in topical sections on teletraffic, traffic characterization and modeling, 3G/UMTS, sensor networks, WLAN, QoS, MANETs, lower layer techniques, PAN technologies, and TCP.

Author : Mário Marques Freire,Pascal Lorenz,Mike Myung-Ok Lee
Publisher : Springer
Page : 586 pages
File Size : 53,8 Mb
Release : 2004-03-06
Category : Computers
ISBN : 9783540450764

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High-Speed Networks and Multimedia Communications by Mário Marques Freire,Pascal Lorenz,Mike Myung-Ok Lee Pdf

The refereed proceedings of the 6th IEEE International Conference on High Speed Networking and Multimedia Communication, HSNMC 2003, held in Estoril, Portugal in July 2003. The 57 revised full papers presented were carefully reviewed and selected from 105 submissions. The papers are organized in topical sections on integrated differentiated services, multicasting, peer-to-peer networking, quality of service, QoS, network and information management, WDM networks, mobile and wireless networks, video, CDMA, real time issues and protocols for IP networks, multimedia streaming, TCP performance, voice over IP, and traffic models.