Cambridge Tracts in Mathematics


Author: Jean Bertoin
Publisher: Cambridge University Press
ISBN: 9780521646321
Category: Mathematics
Page: 266
View: 6035
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This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.

Lévy Processes

Theory and Applications
Author: Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
Publisher: Springer Science & Business Media
ISBN: 1461201977
Category: Mathematics
Page: 418
View: 8203
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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.

XII Symposium of Probability and Stochastic Processes

Merida, Mexico, November 16–20, 2015
Author: Daniel Hernández-Hernández,Juan Carlos Pardo,Victor Rivero
Publisher: Springer
ISBN: 3319776436
Category: Mathematics
Page: 234
View: 2875
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This volume contains the proceedings of the XII Symposium of Probability and Stochastic Processes which took place at Universidad Autonoma de Yucatan in Merida, Mexico, on November 16–20, 2015. This meeting was the twelfth meeting in a series of ongoing biannual meetings aimed at showcasing the research of Mexican probabilists as well as promote new collaborations between the participants. The book features articles drawn from different research areas in probability and stochastic processes, such as: risk theory, limit theorems, stochastic partial differential equations, random trees, stochastic differential games, stochastic control, and coalescence. Two of the main manuscripts survey recent developments on stochastic control and scaling limits of Markov-branching trees, written by Kazutoshi Yamasaki and Bénédicte Haas, respectively. The research-oriented manuscripts provide new advances in active research fields in Mexico. The wide selection of topics makes the book accessible to advanced graduate students and researchers in probability and stochastic processes.

Exotic Option Pricing and Advanced Lévy Models


Author: Andreas Kyprianou,Wim Schoutens,Paul Wilmott
Publisher: John Wiley & Sons
ISBN: 0470017201
Category: Business & Economics
Page: 344
View: 8416
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Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward

Lévy Processes in Lie Groups


Author: Ming Liao
Publisher: Cambridge University Press
ISBN: 9780521836531
Category: Mathematics
Page: 266
View: 8717
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Up-to-the minute research on important stochastic processes.

Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 4664
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Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion


Author: Horst Osswald
Publisher: Cambridge University Press
ISBN: 1107016142
Category: Mathematics
Page: 407
View: 8019
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After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.

The Journal of Derivatives


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Futures
Page: N.A
View: 7151
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SIAM Journal on Control and Optimization


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Automatic control
Page: N.A
View: 2168
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ASTIN Bulletin


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Insurance
Page: N.A
View: 5658
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Annales de l'I.H.P.

Probabilités et statistiques
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Probabilities
Page: N.A
View: 6212
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The Lévy Laplacian


Author: M. N. Feller
Publisher: Cambridge University Press
ISBN: 9781139447966
Category: Mathematics
Page: N.A
View: 526
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The Lévy Laplacian is an infinite-dimensional generalization of the well-known classical Laplacian. The theory has become well developed in recent years and this book was the first systematic treatment of the Lévy–Laplace operator. The book describes the infinite-dimensional analogues of finite-dimensional results, and more especially those features which appear only in the generalized context. It develops a theory of operators generated by the Lévy Laplacian and the symmetrized Lévy Laplacian, as well as a theory of linear and nonlinear equations involving it. There are many problems leading to equations with Lévy Laplacians and to Lévy–Laplace operators, for example superconductivity theory, the theory of control systems, the Gauss random field theory, and the Yang–Mills equation. The book is complemented by an exhaustive bibliography. The result is a work that will be valued by those working in functional analysis, partial differential equations and probability theory.

Internationale Mathematische Nachrichten


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
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Probability on Real Lie Algebras


Author: Uwe Franz,Nicolas Privault
Publisher: Cambridge University Press
ISBN: 110712865X
Category: Mathematics
Page: 302
View: 3443
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This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.

Nonlinear Markov Processes and Kinetic Equations


Author: Vassili N. Kolokoltsov
Publisher: Cambridge University Press
ISBN: 1139489739
Category: Mathematics
Page: N.A
View: 1633
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A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.

Asymptotische Gesetƶe der Wahrscheinlichkeitsrechnung


Author: A. Khintchine
Publisher: Springer-Verlag
ISBN: 364249742X
Category: Computers
Page: 79
View: 4090
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.