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Stable Processes And Related Topics
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Book Synopsis Potential Analysis of Stable Processes and its Extensions by : Krzysztof Bogdan
Download or read book Potential Analysis of Stable Processes and its Extensions written by Krzysztof Bogdan and published by Springer Science & Business Media. This book was released on 2009-07-14 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schrödinger operators. The authors focus on classes of stable and related processes that contain the Brownian motion as a special case. This is the first book devoted to the probabilistic potential theory of stable stochastic processes, and, from the analytical point of view, of the fractional Laplacian. The introduction is accessible to non-specialists and provides a general presentation of the fundamental objects of the theory. Besides recent and deep scientific results the book also provides a didactic approach to its topic, as all chapters have been tested on a wide audience, including young mathematicians at a CNRS/HARP Workshop, Angers 2006. The reader will gain insight into the modern theory of stable and related processes and their potential analysis with a theoretical motivation for the study of their fine properties.
Book Synopsis Stable Processes and Related Topics by : Cambanis
Download or read book Stable Processes and Related Topics written by Cambanis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Processes and Related Topics by : Stamatis Cambanis
Download or read book Stochastic Processes and Related Topics written by Stamatis Cambanis and published by Springer Science & Business Media. This book was released on 1998 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Representation and Structure of Stable Self-Similar Processes.- Three Elementary Proofs of the Central Limit Theorem with Applications to Random Sums.- Almost Everywhere Convergence and SLLN Under Rearrangements.- Sufficient Conditions for the Existence of Conditional Moments of Stable Random Variables.- How Heavy are the Tails of a Stationary HARCH(k) Process? A Study of the Moments.- Use of Stochastic Comparisons in Communication Networks.- On the Conditional Variance-Covariance of Stable Random Vectors, II.- Interacting Particle Approximation for Fractal Burgers Equation.- Optimal Transformations for Prediction in Continuous-Time Stochastic Processes.- Algebraic Methods Toward Higher-Order Probability Inequalities.- Comparison and Deviation from a Representation Formula.- Components of the Strong Markov Property.- The Russian Options.- Cycle Representations of Markov Processes: An Application to Rotational Partitions.- On Extreme Values in Stationary Random Fields.- Norming Operators for Operator-Self-Similar Processes.- Multivariate Probability Density and Regression Functions Estimation of Continuous-time Stationary Processes from Discrete-time Data.- Tracing the Path of a Wright-Fisher Process with One-way Mutation in the Case of a Large Deviation.- A Distribution Inequality for Martingales with Bounded Symmetric Differences.- Moment Comparison of Multilinear Forms in Stable and Semistable Random Variables with Application to Semistable Multiple Integrals.- Global Dependency Measure for Sets of Random Elements: "The Italian Problem" and Some Consequences.
Book Synopsis Stable Processes and Related Topics by : 3Island Press
Download or read book Stable Processes and Related Topics written by 3Island Press and published by . This book was released on 1991-05-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stable Processes and Related Topics by : Stamatis Cambanis
Download or read book Stable Processes and Related Topics written by Stamatis Cambanis and published by . This book was released on 1991-01-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stable Non-Gaussian Random Processes by : Gennady Samoradnitsky
Download or read book Stable Non-Gaussian Random Processes written by Gennady Samoradnitsky and published by Routledge. This book was released on 2017-11-22 with total page 632 pages. 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.
Book Synopsis Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes by : Aleksand Janicki
Download or read book Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes written by Aleksand Janicki and published by CRC Press. This book was released on 2021-07-28 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents new computer methods in approximation, simulation, and visualization for a host of alpha-stable stochastic processes.
Book Synopsis Stochastic Processes and Related Topics by : Ioannis Karatzas
Download or read book Stochastic Processes and Related Topics written by Ioannis Karatzas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last twenty years extensive research has been devoted to a better understanding of the stable and other closely related infinitely divisible mod els. Stamatis Cambanis, a distinguished educator and researcher, played a special leadership role in the development of these research efforts, particu larly related to stable processes from the early seventies until his untimely death in April '95. This commemorative volume consists of a collection of research articles devoted to reviewing the state of the art of this and other rapidly developing research and to explore new directions of research in these fields. The volume is a tribute to the Life and Work of Stamatis by his students, friends, and colleagues whose personal and professional lives he has deeply touched through his generous insights and dedication to his profession. Before the idea of this volume was conceived, two conferences were held in the memory of Stamatis. The first was organized by the University of Athens and the Athens University of Economics and was held in Athens during December 18-19, 1995. The second was a significant part of a Spe cial IMS meeting held at the campus of the University of North Carolina at Chapel Hill during October 17-19, 1996. It is the selfless effort of sev eral people that brought about these conferences. We believe that this is an appropriate place to acknowledge their effort; and on behalf of all the participants, we extend sincere thanks to all these persons.
Book Synopsis Large Deviations for Stochastic Processes by : Jin Feng
Download or read book Large Deviations for Stochastic Processes written by Jin Feng and published by American Mathematical Soc.. This book was released on 2006 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are de
Book Synopsis Stable Lévy Processes via Lamperti-Type Representations by : Andreas E. Kyprianou
Download or read book Stable Lévy Processes via Lamperti-Type Representations written by Andreas E. Kyprianou and published by Cambridge University Press. This book was released on 2022-04-07 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stable Lévy processes lie at the intersection of Lévy processes and self-similar Markov processes. Processes in the latter class enjoy a Lamperti-type representation as the space-time path transformation of so-called Markov additive processes (MAPs). This completely new mathematical treatment takes advantage of the fact that the underlying MAP for stable processes can be explicitly described in one dimension and semi-explicitly described in higher dimensions, and uses this approach to catalogue a large number of explicit results describing the path fluctuations of stable Lévy processes in one and higher dimensions. Written for graduate students and researchers in the field, this book systemically establishes many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material. Topics explored include first hitting laws for a variety of sets, path conditionings, law-preserving path transformations, the distribution of extremal points, growth envelopes and winding behaviour.
Book Synopsis Stochastic Processes and Related Topics by : Stamatis Cambanis
Download or read book Stochastic Processes and Related Topics written by Stamatis Cambanis and published by . This book was released on 1998-01-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Processes and Related Topics by : Rainer Buckdahn
Download or read book Stochastic Processes and Related Topics written by Rainer Buckdahn and published by CRC Press. This book was released on 2002-05-16 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises selected papers presented at the 12th Winter School on Stochastic Processes and their Applications, which was held in Siegmundsburg, Germany, in March 2000. The contents include Backward Stochastic Differential Equations; Semilinear PDE and SPDE; Arbitrage Theory; Credit Derivatives and Models for Correlated Defaults; Three Intertwined Brownian Topics: Exponential Functionals, Winding Numbers and Local Times. A unique opportunity to read ideas from all the top experts on the subject, Stochastic Processes and Related Topics is intended for postgraduates and researchers working in this area of mathematics and provides a useful source of reference.
Book Synopsis Stochastic Processes by : Stamatis Cambanis
Download or read book Stochastic Processes written by Stamatis Cambanis and published by Springer. This book was released on 1993 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Environmental and Ecological Statistics by : Alan E. Gelfand
Download or read book Handbook of Environmental and Ecological Statistics written by Alan E. Gelfand and published by CRC Press. This book was released on 2019-01-15 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook focuses on the enormous literature applying statistical methodology and modelling to environmental and ecological processes. The 21st century statistics community has become increasingly interdisciplinary, bringing a large collection of modern tools to all areas of application in environmental processes. In addition, the environmental community has substantially increased its scope of data collection including observational data, satellite-derived data, and computer model output. The resultant impact in this latter community has been substantial; no longer are simple regression and analysis of variance methods adequate. The contribution of this handbook is to assemble a state-of-the-art view of this interface. Features: An internationally regarded editorial team. A distinguished collection of contributors. A thoroughly contemporary treatment of a substantial interdisciplinary interface. Written to engage both statisticians as well as quantitative environmental researchers. 34 chapters covering methodology, ecological processes, environmental exposure, and statistical methods in climate science.
Book Synopsis Univariate Stable Distributions by : John P. Nolan
Download or read book Univariate Stable Distributions written by John P. Nolan and published by Springer Nature. This book was released on 2020-09-13 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios. Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice. Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.
Book Synopsis Fractals in Biology and Medicine by : Theo F. Nonnenmacher
Download or read book Fractals in Biology and Medicine written by Theo F. Nonnenmacher and published by Birkhäuser. This book was released on 2013-03-07 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fractals in Biology and Medicine" explores the potential of fractal geometry for describing and understanding biological organisms, their development and growth as well as their structural design and functional properties. It extends these notions to assess changes associated with disease in the hope to contribute to the understanding of pathogenetic processes in medicine. The book is the first comprehensive presentation of the importance of the new concept of fractal geometry for biological and medical sciences. It collates in a logical sequence extended papers based on invited lectures and free communications presented at a symposium in Ascona, Switzerland, attended by leading scientists in this field, among them the originator of fractal geometry, Benoit Mandelbrot. "Fractals in Biology and Medicine" begins by asking how the theoretical construct of fractal geometry can be applied to biomedical sciences and then addresses the role of fractals in the design and morphogenesis of biological organisms as well as in molecular and cell biology. The consideration of fractal structure in understanding metabolic functions and pathological changes is a particularly promising avenue for future research.
Book Synopsis Tempered Stable Distributions by : Michael Grabchak
Download or read book Tempered Stable Distributions written by Michael Grabchak and published by Springer. This book was released on 2016-01-26 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief is concerned with tempered stable distributions and their associated Levy processes. It is a good text for researchers interested in learning about tempered stable distributions. A tempered stable distribution is one which takes a stable distribution and modifies its tails to make them lighter. The motivation for this class comes from the fact that infinite variance stable distributions appear to provide a good fit to data in a variety of situations, but the extremely heavy tails of these models are not realistic for most real world applications. The idea of using distributions that modify the tails of stable models to make them lighter seems to have originated in the influential paper of Mantegna and Stanley (1994). Since then, these distributions have been extended and generalized in a variety of ways. They have been applied to a wide variety of areas including mathematical finance, biostatistics,computer science, and physics.
