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Stable Non-Gaussian Self-Similar Processes with Stationary Increments

2017-08-31 Mathematics
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Release : 2017-08-31
Genre : Mathematics
Kind : eBook
Book Rating : 311/5 ( reviews)

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Book Synopsis Stable Non-Gaussian Self-Similar Processes with Stationary Increments by : Vladas Pipiras

Download or read book Stable Non-Gaussian Self-Similar Processes with Stationary Increments written by Vladas Pipiras. This book was released on 2017-08-31. 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.

Selfsimilar Processes

2009-01-10 Mathematics
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Release : 2009-01-10
Genre : Mathematics
Kind : eBook
Book Rating : 105/5 ( reviews)

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Book Synopsis Selfsimilar Processes by : Paul Embrechts

Download or read book Selfsimilar Processes written by Paul Embrechts. This book was released on 2009-01-10. 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.

Stable Non-Gaussian Random Processes

2017-11-22 Mathematics
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Release : 2017-11-22
Genre : Mathematics
Kind : eBook
Book Rating : 801/5 ( reviews)

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Book Synopsis Stable Non-Gaussian Random Processes by : Gennady Samoradnitsky

Download or read book Stable Non-Gaussian Random Processes written by Gennady Samoradnitsky. This book was released on 2017-11-22. 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.

Advances in Planar Lipid Bilayers and Liposomes

2011-08-09 Science
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Release : 2011-08-09
Genre : Science
Kind : eBook
Book Rating : 620/5 ( reviews)

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Book Synopsis Advances in Planar Lipid Bilayers and Liposomes by : A. Leitmannova Liu

Download or read book Advances in Planar Lipid Bilayers and Liposomes written by A. Leitmannova Liu. This book was released on 2011-08-09. Available in PDF, EPUB and Kindle. Book excerpt: 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

2017-04-18 Mathematics
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Release : 2017-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 198/5 ( reviews)

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Book Synopsis Long-Range Dependence and Self-Similarity by : Vladas Pipiras

Download or read book Long-Range Dependence and Self-Similarity written by Vladas Pipiras. This book was released on 2017-04-18. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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