Levy Matters Ii

Author : Serge Cohen
Publisher : Springer
ISBN 13 : 3642314074
Total Pages : 200 pages
Book Rating : 4.70/5 ( download)

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Download or read book Lévy Matters II written by Serge Cohen and published by Springer. This book was released on 2012-09-14 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters, which is published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The expository articles in this second volume cover two important topics in the area of Lévy processes. The first article by Serge Cohen reviews the most important findings on fractional Lévy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications and simulation techniques. The second article, by Alexey Kuznetsov, Andreas E. Kyprianou, and Victor Rivero, presents an up to date account of the theory and application of scale functions for spectrally negative Lévy processes, including an extensive numerical overview.

Author : Björn Böttcher
Publisher : Springer
ISBN 13 : 3319026844
Total Pages : 199 pages
Book Rating : 4.48/5 ( download)

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Download or read book Lévy Matters III written by Björn Böttcher and published by Springer. This book was released on 2014-01-16 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents recent developments in the area of Lévy-type processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévy-type process: a non-random function which is a counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levy-type processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.

Author : Lars Nørvang Andersen
Publisher : Springer
ISBN 13 : 3319231383
Total Pages : 224 pages
Book Rating : 4.89/5 ( download)

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Download or read book Lévy 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.

Author : David Applebaum
Publisher : Cambridge University Press
ISBN 13 : 1139477986
Total Pages : 461 pages
Book Rating : 4.87/5 ( download)

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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 : Denis Belomestny
Publisher : Springer
ISBN 13 : 3319123734
Total Pages : 286 pages
Book Rating : 4.38/5 ( download)

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Download or read book Lévy Matters IV written by Denis Belomestny and published by Springer. This book was released on 2014-12-05 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to provide an extensive account of the most recent advances in statistics for discretely observed Lévy processes. These days, statistics for stochastic processes is a lively topic, driven by the needs of various fields of application, such as finance, the biosciences, and telecommunication. The three chapters of this volume are completely dedicated to the estimation of Lévy processes, and are written by experts in the field. The first chapter by Denis Belomestny and Markus Reiß treats the low frequency situation, and estimation methods are based on the empirical characteristic function. The second chapter by Fabienne Comte and Valery Genon-Catalon is dedicated to non-parametric estimation mainly covering the high-frequency data case. A distinctive feature of this part is the construction of adaptive estimators, based on deconvolution or projection or kernel methods. The last chapter by Hiroki Masuda considers the parametric situation. The chapters cover the main aspects of the estimation of discretely observed Lévy processes, when the observation scheme is regular, from an up-to-date viewpoint.

Author : Thomas Duquesne
Publisher : Springer Science & Business Media
ISBN 13 : 3642140068
Total Pages : 216 pages
Book Rating : 4.68/5 ( download)

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Download or read book Lévy Matters I written by Thomas Duquesne and published by Springer Science & Business Media. This book was released on 2010-09-05 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.

Author : Davar Khoshnevisan
Publisher : Birkhäuser
ISBN 13 : 3319341200
Total Pages : 220 pages
Book Rating : 4.00/5 ( download)

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Download or read book From Lévy-Type Processes to Parabolic SPDEs written by Davar Khoshnevisan and published by Birkhäuser. This book was released on 2016-12-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the lecture notes from two courses given by Davar Khoshnevisan and René Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis. René Schilling’s notes are an expanded version of his course on Lévy and Lévy-type processes, the purpose of which is two-fold: on the one hand, the course presents in detail selected properties of the Lévy processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Lévy-Itô decomposition. On the other, it identifies the infinitesimal generator of the Lévy process as a pseudo-differential operator whose symbol is the characteristic exponent of the process, making it possible to study the properties of Feller processes as space inhomogeneous processes that locally behave like Lévy processes. The presentation is self-contained, and includes dedicated chapters that review Markov processes, operator semigroups, random measures, etc. In turn, Davar Khoshnevisan’s course investigates selected problems in the field of stochastic partial differential equations of parabolic type. More precisely, the main objective is to establish an Invariance Principle for those equations in a rather general setting, and to deduce, as an application, comparison-type results. The framework in which these problems are addressed goes beyond the classical setting, in the sense that the driving noise is assumed to be a multiplicative space-time white noise on a group, and the underlying elliptic operator corresponds to a generator of a Lévy process on that group. This implies that stochastic integration with respect to the above noise, as well as the existence and uniqueness of a solution for the corresponding equation, become relevant in their own right. These aspects are also developed and supplemented by a wealth of illustrative examples.

Author : Franziska Kühn
Publisher : Springer
ISBN 13 : 3319608886
Total Pages : 245 pages
Book Rating : 4.84/5 ( download)

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Download or read book Lévy Matters VI written by Franziska Kühn and published by Springer. This book was released on 2017-10-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting some recent results on the construction and the moments of Lévy-type processes, the focus of this volume is on a new existence theorem, which is proved using a parametrix construction. Applications range from heat kernel estimates for a class of Lévy-type processes to existence and uniqueness theorems for Lévy-driven stochastic differential equations with Hölder continuous coefficients. Moreover, necessary and sufficient conditions for the existence of moments of Lévy-type processes are studied and some estimates on moments are derived. Lévy-type processes behave locally like Lévy processes but, in contrast to Lévy processes, they are not homogeneous in space. Typical examples are processes with varying index of stability and solutions of Lévy-driven stochastic differential equations. This is the sixth volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject, with special emphasis on the non-Brownian world.

Author : Naomi Levy
Publisher : Harmony
ISBN 13 : 0385531702
Total Pages : 258 pages
Book Rating : 4.02/5 ( download)

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Download or read book Hope Will Find You written by Naomi Levy and published by Harmony. This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this moving, personal work, Levy tells of the painful circumstances she endured with her young daughter's illness, how they grew together, and ultimately how much Levy learned from her daughter's example.

Author : Joanne Levy
Publisher : Orca Book Publishers
ISBN 13 : 1459812484
Total Pages : 166 pages
Book Rating : 4.82/5 ( download)

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Download or read book The Sun Will Come Out written by Joanne Levy and published by Orca Book Publishers. This book was released on 2021-04-13 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Key Selling Points A sweet summer camp story about a painfully shy girl who meets a boy with a rare genetic condition. The book explores themes of facing your fears and the nature of true friendship. One of the main characters has progeria, a genetic condition that causes premature aging. Most children who have this don’t live past age 14. This story had its genesis in a terrible summer camp experience for the author. The book has a happy ending. Bea and her new friends stay in touch after summer is over.