Stable Non-Gaussian Self-Similar Processes with Stationary Increments

Stable Non-Gaussian Self-Similar Processes with Stationary Increments
Author: Vladas Pipiras
Publisher: Springer
Total Pages: 143
Release: 2017-08-31
Genre: Mathematics
ISBN: 3319623311

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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.

Selfsimilar Processes

Selfsimilar Processes
Author: Paul Embrechts
Publisher: Princeton University Press
Total Pages: 125
Release: 2009-01-10
Genre: Mathematics
ISBN: 1400825105

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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.

Stable Non-Gaussian Random Processes

Stable Non-Gaussian Random Processes
Author: Gennady Samoradnitsky
Publisher: Routledge
Total Pages: 632
Release: 2017-11-22
Genre: Mathematics
ISBN: 1351414801

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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.

Advances in Planar Lipid Bilayers and Liposomes

Advances in Planar Lipid Bilayers and Liposomes
Author: A. Leitmannova Liu
Publisher: Academic Press
Total Pages: 280
Release: 2011-08-09
Genre: Science
ISBN: 0080921620

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Advances in Planar Lipid Bilayers and Liposomes, Volume 7, continues to include invited chapters on a broad range of topics, covering both main arrangements of the reconstituted system, namely planar lipid bilayers and spherical liposomes. The invited authors present the latest results in this exciting multidisciplinary field of their own research group. Many of the contributors working in both fields over many decades were in close collaboration with the late Prof. H. Ti Tien, the founding editor of this book series. There are also chapters written by some of the younger generation of scientists included in this series. This volume keeps in mind the broader goal with both systems, planar lipid bilayers and spherical liposomes, which is the further development of this interdisciplinary field worldwide. * Contributions from newcomers and established and experienced researchers * Exploring theoretically and experimentally the planar lipid bilayer systems and spherical liposomes * Indispensable source of information for new scientists

Long-Range Dependence and Self-Similarity

Long-Range Dependence and Self-Similarity
Author: Vladas Pipiras
Publisher: Cambridge University Press
Total Pages: 693
Release: 2017-04-18
Genre: Mathematics
ISBN: 1108210198

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This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and self-similarity; central and non-central limit theorems for long-range dependent series, and the limiting Hermite processes; fractional Brownian motion and its stochastic calculus; several celebrated decompositions of fractional Brownian motion; multidimensional models for long-range dependence and self-similarity; and maximum likelihood estimation methods for long-range dependent time series. Designed for graduate students and researchers, each chapter of the book is supplemented by numerous exercises, some designed to test the reader's understanding, while others invite the reader to consider some of the open research problems in the field today.

Two Classes of Self-Similar Stable Processes with Stationary Increments

Two Classes of Self-Similar Stable Processes with Stationary Increments
Author: Stamatis Cambanis
Publisher:
Total Pages: 34
Release: 1988
Genre:
ISBN:

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Two disjoint classes of self-similar symmetric stable processes with stationary increments are studied. The first class consists of linear fractional stable processes, which are related to moving average stable processes, and the second class consists of harmonizable fractional stable processes, which are connected to harmonizable stationary stable processes. The domain of attraction of the harmonizable fractional stable processes is also discussed. Keywords: Self similar processes; Stable processes; Harmonizable fractional processes; Domain of attraction; Linear fractional process.

Encyclopedia of Financial Models, Volume III

Encyclopedia of Financial Models, Volume III
Author: Frank J. Fabozzi
Publisher: John Wiley & Sons
Total Pages: 1060
Release: 2012-09-20
Genre: Business & Economics
ISBN: 1118539834

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Volume 3 of the Encyclopedia of Financial Models The need for serious coverage of financial modeling has never been greater, especially with the size, diversity, and efficiency of modern capital markets. With this in mind, the Encyclopedia of Financial Models has been created to help a broad spectrum of individuals—ranging from finance professionals to academics and students—understand financial modeling and make use of the various models currently available. Incorporating timely research and in-depth analysis, Volume 3 of the Encyclopedia of Financial Models covers both established and cutting-edge models and discusses their real-world applications. Edited by Frank Fabozzi, this volume includes contributions from global financial experts as well as academics with extensive consulting experience in this field. Organized alphabetically by category, this reliable resource consists of forty-four informative entries and provides readers with a balanced understanding of today’s dynamic world of financial modeling. Volume 3 covers Mortgage-Backed Securities Analysis and Valuation, Operational Risk, Optimization Tools, Probability Theory, Risk Measures, Software for Financial Modeling, Stochastic Processes and Tools, Term Structure Modeling, Trading Cost Models, and Volatility Emphasizes both technical and implementation issues, providing researchers, educators, students, and practitioners with the necessary background to deal with issues related to financial modeling The 3-Volume Set contains coverage of the fundamentals and advances in financial modeling and provides the mathematical and statistical techniques needed to develop and test financial models Financial models have become increasingly commonplace, as well as complex. They are essential in a wide range of financial endeavors, and the Encyclopedia of Financial Models will help put them in perspective.

Trends In Probability And Related Analysis - Proceedings Of Sap'96

Trends In Probability And Related Analysis - Proceedings Of Sap'96
Author: N Kono
Publisher: World Scientific
Total Pages: 365
Release: 1997-10-31
Genre:
ISBN: 981454552X

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This proceedings volume reflects the current interest — especially of researchers in the Asia-Pacific region — in probability theory and related theory of analysis and statistics. It contains the papers of the two survey speakers, and of some other speakers and researchers. It brings out the theme of SAP, an international meeting on some aspects of probability, analysis and their interplay.

Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes

Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes
Author: Aleksand Janicki
Publisher: CRC Press
Total Pages: 376
Release: 2021-07-28
Genre: Mathematics
ISBN: 1000445070

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Presents new computer methods in approximation, simulation, and visualization for a host of alpha-stable stochastic processes.

Fractals: Theory and Applications in Engineering

Fractals: Theory and Applications in Engineering
Author: Michel Dekking
Publisher: Springer Science & Business Media
Total Pages: 336
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1447108736

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Owing to the rapid emergence and growth of techniques in the engineering application of fractals, it has become necessary to gather the most recent advances on a regular basis. This book is a continuation of the first volume - published in 1997 - but contains interesting developments. A major point is that mathematics has become more and more involved in the definition and use of fractal models. It seems that the time of the qualitative observation of fractal phenomena has gone. Now the main models are strongly based upon theoretical arguments. Fractals: Theory and Applications in Engineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.