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Lévy Processes

Theory and Applications

Editors: Barndorff-Nielsen, Ole E., Mikosch, Thomas, Resnick, Sidney I. (Eds.)

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  • ISBN 978-1-4612-0197-7
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About this book

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.

 

Reviews

"This volume presents a useful summary of some of the recent scientific developments concerning Lévy processes. Both introductory and more advanced articles are included. The interested researcher will get a good overview of 'where the action is' whereas students will find numerous interesting research topics to work on . . . I am convinced that the text will contribute further to making stochastic models based on general Lévy processes even more popular. I, therefore, take pleasure in recommending this volume to all interested readers." —ISI Short Book Reviews


Table of contents (18 chapters)

Table of contents (18 chapters)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-1-4612-0197-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
Softcover $119.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Lévy Processes
Book Subtitle
Theory and Applications
Editors
  • Ole E. Barndorff-Nielsen
  • Thomas Mikosch
  • Sidney I. Resnick
Copyright
2001
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-1-4612-0197-7
DOI
10.1007/978-1-4612-0197-7
Hardcover ISBN
978-0-8176-4167-2
Softcover ISBN
978-1-4612-6657-0
Edition Number
1
Number of Pages
XI, 418
Topics