Lévy Matters Iii

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Lévy Matters III

Björn Böttcher,René Schilling,Jian Wang
L vy Matters III Book PDF

Author : Björn Böttcher,René Schilling,Jian Wang
Publisher : Springer
Page : 199 pages
File Size : 45,9 Mb
Release : 2014-01-16
Category : Mathematics
ISBN : 9783319026848

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Lévy Matters III by Björn Böttcher,René Schilling,Jian Wang Pdf

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.

Lévy Matters II

Serge Cohen,Alexey Kuznetsov,Andreas E. Kyprianou,Victor Rivero
L vy Matters II Book PDF

Author : Serge Cohen,Alexey Kuznetsov,Andreas E. Kyprianou,Victor Rivero
Publisher : Springer
Page : 186 pages
File Size : 46,6 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 9783642314070

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Lévy Matters II by Serge Cohen,Alexey Kuznetsov,Andreas E. Kyprianou,Victor Rivero Pdf

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.

Lévy Matters V

Lars Nørvang Andersen,Søren Asmussen,Frank Aurzada,Peter W. Glynn,Makoto Maejima,Mats Pihlsgård,Thomas Simon
L vy Matters V Book PDF

Author : Lars Nørvang Andersen,Søren Asmussen,Frank Aurzada,Peter W. Glynn,Makoto Maejima,Mats Pihlsgård,Thomas Simon
Publisher : Springer
Page : 224 pages
File Size : 55,8 Mb
Release : 2015-10-24
Category : Mathematics
ISBN : 9783319231389

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Lévy Matters V by Lars Nørvang Andersen,Søren Asmussen,Frank Aurzada,Peter W. Glynn,Makoto Maejima,Mats Pihlsgård,Thomas Simon Pdf

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.

Lévy Matters II

Serge Cohen,Alexey Kuznetsov,Andreas E. Kyprianou,Victor Rivero
L vy Matters II Book PDF

Author : Serge Cohen,Alexey Kuznetsov,Andreas E. Kyprianou,Victor Rivero
Publisher : Springer
Page : 186 pages
File Size : 50,7 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 3642314074

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Lévy Matters II by Serge Cohen,Alexey Kuznetsov,Andreas E. Kyprianou,Victor Rivero Pdf

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.

Lévy Matters

Serge Cohen
L vy Matters Book PDF

Author : Serge Cohen
Publisher : Unknown
Page : 186 pages
File Size : 47,9 Mb
Release : 2012
Category : Lévy processes
ISBN : OCLC:988785622

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Lévy Matters by Serge Cohen Pdf

"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."--Publisher's website.

Lévy Matters IV

Denis Belomestny,Fabienne Comte,Valentine Genon-Catalot,Hiroki Masuda,Markus Reiß
L vy Matters IV Book PDF

Author : Denis Belomestny,Fabienne Comte,Valentine Genon-Catalot,Hiroki Masuda,Markus Reiß
Publisher : Springer
Page : 286 pages
File Size : 41,5 Mb
Release : 2014-12-05
Category : Mathematics
ISBN : 9783319123738

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Lévy Matters IV by Denis Belomestny,Fabienne Comte,Valentine Genon-Catalot,Hiroki Masuda,Markus Reiß Pdf

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.

Lévy Matters VI

Franziska Kühn
L vy Matters VI Book PDF

Author : Franziska Kühn
Publisher : Springer
Page : 245 pages
File Size : 41,5 Mb
Release : 2017-10-05
Category : Mathematics
ISBN : 9783319608884

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Lévy Matters VI by Franziska Kühn Pdf

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.

Lévy Matters I

Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
L vy Matters I Book PDF

Author : Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
Publisher : Springer
Page : 206 pages
File Size : 50,5 Mb
Release : 2010-09-02
Category : Mathematics
ISBN : 9783642140075

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Lévy Matters I by Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab Pdf

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.

Lévy Matters I

Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
L vy Matters I Book PDF

Author : Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 51,8 Mb
Release : 2010-09-05
Category : Mathematics
ISBN : 9783642140068

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Lévy Matters I by Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab Pdf

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.

From Lévy-Type Processes to Parabolic SPDEs

Davar Khoshnevisan,René Schilling
From L vy Type Processes to Parabolic SPDEs Book PDF

Author : Davar Khoshnevisan,René Schilling
Publisher : Birkhäuser
Page : 220 pages
File Size : 53,9 Mb
Release : 2016-12-22
Category : Mathematics
ISBN : 9783319341200

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From Lévy-Type Processes to Parabolic SPDEs by Davar Khoshnevisan,René Schilling Pdf

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.

Pricing Derivatives Under Lévy Models

Andrey Itkin
Pricing Derivatives Under L vy Models Book PDF

Author : Andrey Itkin
Publisher : Birkhäuser
Page : 308 pages
File Size : 44,7 Mb
Release : 2017-02-27
Category : Mathematics
ISBN : 9781493967926

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Pricing Derivatives Under Lévy Models by Andrey Itkin Pdf

This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method. Written for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. It can also be used as an advance course on modern finite-difference methods or computational finance.

Lévy Processes

Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
L vy Processes Book PDF

Author : Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201977

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Lévy Processes by Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick Pdf

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.

Most of Me

Robyn Levy
Most of Me Book PDF

Author : Robyn Levy
Publisher : Greystone Books Ltd
Page : 256 pages
File Size : 47,6 Mb
Release : 2012
Category : Biography & Autobiography
ISBN : 9781553656326

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Most of Me by Robyn Levy Pdf

The author recounts her devastating medical diagnoses of Parkinson's disease and two lumps in her breast which required a mastectomy.

Berne & Levy Principles of Physiology E-Book

Matthew N. Levy,Bruce M. Koeppen,Bruce A. Stanton
Berne Levy Principles of Physiology E Book Book PDF

Author : Matthew N. Levy,Bruce M. Koeppen,Bruce A. Stanton
Publisher : Elsevier Health Sciences
Page : 835 pages
File Size : 52,9 Mb
Release : 2005-09-09
Category : Medical
ISBN : 9780323064576

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Berne & Levy Principles of Physiology E-Book by Matthew N. Levy,Bruce M. Koeppen,Bruce A. Stanton Pdf

Here's a succinct, up-to-date summary of the physiological processes that take place in the human body, written in a straightforward and easy-to-understand manner. Derived from Berne et al.'s more lengthy text, Physiology, 5th Edition, it concisely and efficiently covers all of the most need-to-know concepts in the field. Updates include discussions of how the most recent findings in molecular biology and genetics affect our knowledge of physiology. A wealth of case examples, full-color artwork, review questions with answers, and boxes, tables, and graphs help readers to easily and thoroughly master the material. The smart way to study! Elsevier titles with STUDENT CONSULT will help you master difficult concepts and study more efficiently in print and online! Perform rapid searches. Integrate bonus content from other disciplines. Download text to your handheld device. And a lot more. Each STUDENT CONSULT title comes with full text online, a unique image library, case studies, USMLE style questions, and online note-taking to enhance your learning experience. Provides shaded "clinical boxes" to demonstrate abstract concepts' relevance to human physiological phenomena. Offers case examples that show how physiological processes respond to various stimuli or to pathological processes. Delivers hundreds of full-color illustrations that make complex physiological principles easy to grasp quickly. Includes abundant graphs, figures, and tables that display information at a glance. Presents review questions and answers that allow readers to evaluate their comprehension. Incorporates a great deal of new information on how new discoveries in molecular biology and genetics affect our understanding of human physiology. Includes access to www.studentconsult.com — with the full text of the book online, integration links to relevant material from other STUDENT CONSULT texts, online self-assessment activities, a community center, and other valuable features.

Lévy Processes and Stochastic Calculus

David Applebaum
L vy Processes and Stochastic Calculus Book PDF

Author : David Applebaum
Publisher : Cambridge University Press
Page : 461 pages
File Size : 48,8 Mb
Release : 2009-04-30
Category : Mathematics
ISBN : 9781139477987

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Lévy Processes and Stochastic Calculus by David Applebaum Pdf

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.