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Fluctuation Theory for Lévy Processes

Ecole d'Eté de Probabilités de Saint-Flour XXXV - 2005

  • Ronald A. Doney
  • Jean Picard

Part of the Lecture Notes in Mathematics book series (LNM, volume 1897)

Table of contents

About this book

Introduction

Lévy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul Lévy, who made the connection with infinitely divisible distributions and described their structure. They form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, ... and of course finance, where the feature that they include examples having "heavy tails" is particularly important. Their sample path behaviour poses a variety of difficult and fascinating problems. Such problems, and also some related distributional problems, are addressed in detail in these notes that reflect the content of the course given by R. Doney in St. Flour in 2005.

Keywords

Ladder processes Lévy process Lévy processes Reflected process Sample path behaviour Wiener-Hopf factorisation local time

Authors and affiliations

  • Ronald A. Doney
    • 1
  1. 1.School of MathematicsUniversity of ManchesterManchesterUK

Editors and affiliations

  • Jean Picard
    • 1
  1. 1.Laboratoire de Mathématiques AppliquéesUniversité Blaise Pascal (Clermont-Ferrand)Aubière CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-48511-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-48510-0
  • Online ISBN 978-3-540-48511-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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