Universitext

Fluctuations of Lévy Processes with Applications

Introductory Lectures

Authors: Kyprianou, Andreas E.

  • Addresses recent developments in the potential analysis of subordinators
  • Includes an extensive overview of the classical and modern theory of positive self-similar Markov processes
  • Each chapter has a comprehensive set of exercises
see more benefits

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-642-37632-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-3-642-37631-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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.


About the authors

Andreas Kyprianou has a degree in Mathematics from the University of Oxford and a Ph.D. in Probability Theory from The University of Sheffield. He is currently a Professor of Probability at the University of Bath, having held academic positions in Mathematics and Statistics Departments at the London School of Economics, Edinburgh University, Utrecht University and Heriot-Watt University, besides working for nearly two years as a research mathematician in the oil industry. His research is focused on pure and applied probability.

Reviews

“The book grew out of lectures pitched at an advanced undergraduate or beginning graduate audience, the prerequisite being a course on abstract Lebesgue integration and a good foundation in probability theory … . Fluctuations of Lévy processes is an interesting book and it is currently the best introduction for the novice to this important topic.” (René L. Schilling, Mathematical Reviews, April, 2015)


Video

Table of contents (13 chapters)

  • Lévy Processes and Applications

    Kyprianou, Andreas E.

    Pages 1-33

  • The Lévy–Itô Decomposition and Path Structure

    Kyprianou, Andreas E.

    Pages 35-69

  • More Distributional and Path-Related Properties

    Kyprianou, Andreas E.

    Pages 71-89

  • General Storage Models and Paths of Bounded Variation

    Kyprianou, Andreas E.

    Pages 91-113

  • Subordinators at First Passage and Renewal Measures

    Kyprianou, Andreas E.

    Pages 115-152

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-642-37632-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-3-642-37631-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Fluctuations of Lévy Processes with Applications
Book Subtitle
Introductory Lectures
Authors
Series Title
Universitext
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-37632-0
DOI
10.1007/978-3-642-37632-0
Softcover ISBN
978-3-642-37631-3
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XVIII, 455
Number of Illustrations and Tables
26 b/w illustrations
Topics