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Author : Sato Ken-Iti
Publisher : Cambridge University Press
ISBN 13 : 9780521553025
Total Pages : 504 pages
Book Rating : 4.5/5 (53 download)
Download or read book Lévy 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:
Author : 健一·佐藤
Publisher :
ISBN 13 : 9780521553025
Total Pages : 486 pages
Book Rating : 4.5/5 (53 download)
Download or read book Lévy 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.
Author : Alfonso Rocha-Arteaga
Publisher : Springer Nature
ISBN 13 : 3030227006
Total Pages : 135 pages
Book Rating : 4.0/5 (32 download)
Download or read book Topics in Infinitely Divisible Distributions and Lévy 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.
Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
ISBN 13 : 3642376320
Total Pages : 455 pages
Book Rating : 4.6/5 (423 download)
Download or read book Fluctuations of Lévy 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 455 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.
Author : Alfonso Rocha Arteaga
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.E/5 ( download)
Download or read book Topics in Infinitely Divisible Distributions and Lévy 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:
Author : Ole E Barndorff-Nielsen
Publisher : Springer Science & Business Media
ISBN 13 : 1461201977
Total Pages : 418 pages
Book Rating : 4.4/5 (612 download)
Download or read book Lévy 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 418 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.
Author : Kiyosi Ito
Publisher : Springer Science & Business Media
ISBN 13 : 3662100657
Total Pages : 246 pages
Book Rating : 4.6/5 (621 download)
Download or read book Stochastic Processes written by Kiyosi Ito and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with independent increments (the Lévy-Itô decomposition). It also contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. In addition, 70 exercises and their complete solutions are included.
Author : Ronald A. Doney
Publisher : Springer
ISBN 13 : 3540485112
Total Pages : 155 pages
Book Rating : 4.5/5 (44 download)
Download or read book Fluctuation Theory for Lévy Processes written by Ronald A. Doney and published by Springer. This book was released on 2007-04-25 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes, that is, processes in continuous time with stationary and independent increments, form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, and of course finance, where they include particularly important examples having "heavy tails." Their sample path behaviour poses a variety of challenging and fascinating problems, which are addressed in detail.
Author : David Applebaum
Publisher : Cambridge University Press
ISBN 13 : 1139477986
Total Pages : 461 pages
Book Rating : 4.1/5 (394 download)
Download or read book Lévy 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.
Author : Loïc Chaumont
Publisher : Springer Nature
ISBN 13 : 3030833097
Total Pages : 354 pages
Book Rating : 4.0/5 (38 download)
Download or read book A Lifetime of Excursions Through Random Walks and Lévy Processes written by Loïc Chaumont and published by Springer Nature. This book was released on 2022-01-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection honours Ron Doney’s work and includes invited articles by his collaborators and friends. After an introduction reviewing Ron Doney’s mathematical achievements and how they have influenced the field, the contributed papers cover both discrete-time processes, including random walks and variants thereof, and continuous-time processes, including Lévy processes and diffusions. A good number of the articles are focused on classical fluctuation theory and its ramifications, the area for which Ron Doney is best known.
Author : Jean Bertoin
Publisher : Cambridge University Press
ISBN 13 : 9780521646321
Total Pages : 292 pages
Book Rating : 4.6/5 (463 download)
Download or read book Cambridge Tracts in Mathematics written by Jean Bertoin and published by Cambridge University Press. This book was released on 1996 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.
Author : Ming Liao
Publisher : Cambridge University Press
ISBN 13 : 9780521836531
Total Pages : 292 pages
Book Rating : 4.8/5 (365 download)
Download or read book Lévy Processes in Lie Groups written by Ming Liao and published by Cambridge University Press. This book was released on 2004-05-10 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Up-to-the minute research on important stochastic processes.
Author : Andreas E. Kyprianou
Publisher : Cambridge University Press
ISBN 13 : 1108572162
Total Pages : 486 pages
Book Rating : 4.1/5 (85 download)
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.
Author : Bert E. Fristedt
Publisher : Springer Science & Business Media
ISBN 13 : 1489928375
Total Pages : 775 pages
Book Rating : 4.4/5 (899 download)
Download or read book A Modern Approach to Probability Theory written by Bert E. Fristedt and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.
Author : Michael Unser
Publisher : Cambridge University Press
ISBN 13 : 1107058546
Total Pages : 387 pages
Book Rating : 4.1/5 (7 download)
Download or read book An Introduction to Sparse Stochastic Processes written by Michael Unser and published by Cambridge University Press. This book was released on 2014-08-21 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed guide to sparsity, providing a description of their transform-domain statistics and applying the models to practical algorithms.
Author : Svetlozar T. Rachev
Publisher : John Wiley & Sons
ISBN 13 : 0470937262
Total Pages : 316 pages
Book Rating : 4.4/5 (79 download)
Download or read book Financial Models with Levy Processes and Volatility Clustering written by Svetlozar T. Rachev and published by John Wiley & Sons. This book was released on 2011-02-08 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management In Financial Models with Lévy Processes and Volatility Clustering, the expert author team provides a framework to model the behavior of stock returns in both a univariate and a multivariate setting, providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distribution in financial modeling and the best methodologies for employing it. The book's framework includes the basics of probability distributions and explains the alpha-stable distribution and the tempered stable distribution. The authors also explore discrete time option pricing models, beginning with the classical normal model with volatility clustering to more recent models that consider both volatility clustering and heavy tails. Reviews the basics of probability distributions Analyzes a continuous time option pricing model (the so-called exponential Lévy model) Defines a discrete time model with volatility clustering and how to price options using Monte Carlo methods Studies two multivariate settings that are suitable to explain joint extreme events Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.
Author : Peter Tankov
Publisher : CRC Press
ISBN 13 : 1135437947
Total Pages : 552 pages
Book Rating : 4.1/5 (354 download)
Download or read book Financial Modelling with Jump Processes written by Peter Tankov and published by CRC Press. This book was released on 2003-12-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic
