Download or read book Topics in Infinitely Divisible Distributions and L vy Processes Revised Edition written by Alfonso Rocha-Arteaga and published by Springer Nature. This book was released on 2019-11-02 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with topics in the area of Lévy processes and infinitely divisible distributions such as Ornstein-Uhlenbeck type processes, selfsimilar additive processes and multivariate subordination. These topics are developed around a decreasing chain of classes of distributions Lm, m = 0,1,...,∞, from the class L0 of selfdecomposable distributions to the class L∞ generated by stable distributions through convolution and convergence. The book is divided into five chapters. Chapter 1 studies basic properties of Lm classes needed for the subsequent chapters. Chapter 2 introduces Ornstein-Uhlenbeck type processes generated by a Lévy process through stochastic integrals based on Lévy processes. Necessary and sufficient conditions are given for a generating Lévy process so that the OU type process has a limit distribution of Lm class. Chapter 3 establishes the correspondence between selfsimilar additive processes and selfdecomposable distributions and makes a close inspection of the Lamperti transformation, which transforms selfsimilar additive processes and stationary type OU processes to each other. Chapter 4 studies multivariate subordination of a cone-parameter Lévy process by a cone-valued Lévy process. Finally, Chapter 5 studies strictly stable and Lm properties inherited by the subordinated process in multivariate subordination. In this revised edition, new material is included on advances in these topics. It is rewritten as self-contained as possible. Theorems, lemmas, propositions, examples and remarks were reorganized; some were deleted and others were newly added. The historical notes at the end of each chapter were enlarged. This book is addressed to graduate students and researchers in probability and mathematical statistics who are interested in learning more on Lévy processes and infinitely divisible distributions.
Download or read book L vy Processes and Infinitely Divisible Distributions written by Sato Ken-Iti and published by Cambridge University Press. This book was released on 1999 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Infinite Divisibility of Probability Distributions on the Real Line written by Fred W. Steutel and published by CRC Press. This book was released on 2003-10-03 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite Divisibility of Probability Distributions on the Real Line reassesses classical theory and presents new developments, while focusing on divisibility with respect to convolution or addition of independent random variables. This definitive, example-rich text supplies approximately 100 examples to correspond with all major chapter topics and reviews infinite divisibility in light of the central limit problem. It contrasts infinite divisibility with finite divisibility, discusses the preservation of infinite divisibility under mixing for many classes of distributions, and investigates self-decomposability and stability on the nonnegative reals, nonnegative integers, and the reals.
Download or read book Topics in Probability written by Narahari Prabhu and published by World Scientific. This book was released on 2011 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent research in probability has been concerned with applications such as data mining and finance models. Some aspects of the foundations of probability theory have receded into the background. Yet, these aspects are very important and have to be brought back into prominence.
Download or read book L vy Processes and Infinitely Divisible Distributions written by 健一·佐藤 and published by . This book was released on 1999-11-11 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book is intended to provide the reader with comprehensive basic knowledge of Lévy processes, and at the same time serve as an introduction to stochastic processes in general. No specialist knowledge is assumed and proofs are given in detail. Systematic study is made of stable and semi-stable processes, and the author gives special emphasis to the correspondence between Lévy processes and infinitely divisible distributions. All serious students of random phenomena will find that this book has much to offer. Now in paperback, this corrected edition contains a brand new supplement discussing relevant developments in the area since the book's initial publication.
Download or read book Topics in Infinitely Divisible Distributions and L vy Processes written by Alfonso Rocha-Arteaga and published by . This book was released on 2003 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Infinitely Divisible Point Processes written by Johannes Kerstan and published by John Wiley & Sons. This book was released on 1978 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Preservation of Infinite Divisibility Under Mixing and Related Topics written by F. W. Steutel and published by . This book was released on 1970 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Stein s Method for Infinitely Divisible Laws with Finite First Moment written by Benjamin Arras and published by Springer. This book was released on 2019-04-24 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on quantitative approximation results for weak limit theorems when the target limiting law is infinitely divisible with finite first moment. Two methods are presented and developed to obtain such quantitative results. At the root of these methods stands a Stein characterizing identity discussed in the third chapter and obtained thanks to a covariance representation of infinitely divisible distributions. The first method is based on characteristic functions and Stein type identities when the involved sequence of random variables is itself infinitely divisible with finite first moment. In particular, based on this technique, quantitative versions of compound Poisson approximation of infinitely divisible distributions are presented. The second method is a general Stein's method approach for univariate selfdecomposable laws with finite first moment. Chapter 6 is concerned with applications and provides general upper bounds to quantify the rate of convergence in classical weak limit theorems for sums of independent random variables. This book is aimed at graduate students and researchers working in probability theory and mathematical statistics.
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 296 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 In
Download or read book Infinitely Divisible Point Processes written by Johannes Kerstan and published by . This book was released on with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fluctuations of L vy Processes with Applications written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.
Download or read book L vy Matters I written by Thomas Duquesne and published by Springer. This book was released on 2010-09-02 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.
Download or read book Perspectives in Mathematical Sciences written by Yisong Yang and published by World Scientific. This book was released on 2010 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gun Shy
Download or read book L vy Processes written by Ole E Barndorff-Nielsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.
Download or read book L vy Processes and Stochastic Calculus written by David Applebaum and published by Cambridge University Press. This book was released on 2009-04-30 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Download or read book L vy Matters V written by Lars Nørvang Andersen and published by Springer. This book was released on 2015-10-24 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-chapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lévy processes via stochastic integration. The second chapter, by Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgård, concerns Lévy processes reflected at two barriers, where reflection is formulated à la Skorokhod. These processes can be used to model systems with a finite capacity, which is crucial in many real life situations, a most important quantity being the overflow or the loss occurring at the upper barrier. If a process is killed when crossing the boundary, a natural question concerns its lifetime. Deep formulas from fluctuation theory are the key to many classical results, which are reviewed in the third chapter by Frank Aurzada and Thomas Simon. The main part, however, discusses recent advances and developments in the setting where the process is given either by the partial sum of a random walk or the integral of a Lévy process.
