Two Classes of Self-Similar Stable Processes with Stationary Increments
Title | Two Classes of Self-Similar Stable Processes with Stationary Increments PDF eBook |
Author | Stamatis Cambanis |
Publisher | |
Pages | 34 |
Release | 1988 |
Genre | |
ISBN |
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.
Stable Non-Gaussian Self-Similar Processes with Stationary Increments
Title | Stable Non-Gaussian Self-Similar Processes with Stationary Increments PDF eBook |
Author | Vladas Pipiras |
Publisher | Springer |
Pages | 143 |
Release | 2017-08-31 |
Genre | Mathematics |
ISBN | 3319623311 |
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
Title | Selfsimilar Processes PDF eBook |
Author | Paul Embrechts |
Publisher | Princeton University Press |
Pages | 125 |
Release | 2009-01-10 |
Genre | Mathematics |
ISBN | 1400825105 |
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.
Chaos Expansions, Multiple Wiener-Ito Integrals, and Their Applications
Title | Chaos Expansions, Multiple Wiener-Ito Integrals, and Their Applications PDF eBook |
Author | Christian Houdre |
Publisher | CRC Press |
Pages | 396 |
Release | 1994-04-05 |
Genre | Mathematics |
ISBN | 9780849380723 |
The study of chaos expansions and multiple Wiener-Ito integrals has become a field of considerable interest in applied and theoretical areas of probability, stochastic processes, mathematical physics, and statistics. Divided into four parts, this book features a wide selection of surveys and recent developments on these subjects. Part 1 introduces the concepts, techniques, and applications of multiple Wiener-Ito and related integrals. The second part includes papers on chaos random variables appearing in many limiting theorems. Part 3 is devoted to mixing, zero-one laws, and path continuity properties of chaos processes. The final part presents several applications to stochastic analysis.
Stochastic Processes
Title | Stochastic Processes PDF eBook |
Author | Stamatis Cambanis |
Publisher | Springer Science & Business Media |
Pages | 373 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461579090 |
This volume celebrates the many contributions which Gopinath Kallianpur has made to probability and statistics. It comprises 40 chapters which taken together survey the wide sweep of ideas which have been influenced by Professor Kallianpur's writing and research.
Stable Processes and Related Topics
Title | Stable Processes and Related Topics PDF eBook |
Author | Cambanis |
Publisher | Springer Science & Business Media |
Pages | 329 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1468467786 |
The Workshop on Stable Processes and Related Topics took place at Cor nell University in January 9-13, 1990, under the sponsorship of the Mathemat ical Sciences Institute. It attracted an international roster of probabilists from Brazil, Japan, Korea, Poland, Germany, Holland and France as well as the U. S. This volume contains a sample of the papers presented at the Workshop. All the papers have been refereed. Gaussian processes have been studied extensively over the last fifty years and form the bedrock of stochastic modeling. Their importance stems from the Central Limit Theorem. They share a number of special properties which facilitates their analysis and makes them particularly suitable to statistical inference. The many properties they share, however, is also the seed of their limitations. What happens in the real world away from the ideal Gaussian model? The non-Gaussian world may contain random processes that are close to the Gaussian. What are appropriate classes of nearly Gaussian models and how typical or robust is the Gaussian model amongst them? Moving further away from normality, what are appropriate non-Gaussian models that are sufficiently different to encompass distinct behavior, yet sufficiently simple to be amenable to efficient statistical inference? The very Central Limit Theorem which provides the fundamental justifi cation for approximate normality, points to stable and other infinitely divisible models. Some of these may be close to and others very different from Gaussian models.
Stable Non-Gaussian Random Processes
Title | Stable Non-Gaussian Random Processes PDF eBook |
Author | Gennady Samoradnitsky |
Publisher | Routledge |
Pages | 632 |
Release | 2017-11-22 |
Genre | Mathematics |
ISBN | 1351414801 |
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.