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Lévy Matters III

Lévy-Type Processes: Construction, Approximation and Sample Path Properties

  • Björn Böttcher
  • René Schilling
  • Jian Wang

Part of the Lecture Notes in Mathematics book series (LNM, volume 2099)

Also part of the Lévy Matters book sub series (LEVY, volume 2099)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Björn Böttcher, René Schilling, Jian Wang
    Pages 1-30
  3. Björn Böttcher, René Schilling, Jian Wang
    Pages 31-67
  4. Björn Böttcher, René Schilling, Jian Wang
    Pages 69-98
  5. Björn Böttcher, René Schilling, Jian Wang
    Pages 99-110
  6. Björn Böttcher, René Schilling, Jian Wang
    Pages 111-140
  7. Björn Böttcher, René Schilling, Jian Wang
    Pages 141-165
  8. Björn Böttcher, René Schilling, Jian Wang
    Pages 167-175
  9. Björn Böttcher, René Schilling, Jian Wang
    Pages 177-179
  10. Back Matter
    Pages 181-202

About this book

Introduction

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 the 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.

Keywords

60-02;60J25;60J35;60G17;35S05;60J75;60G48;60G51 Feller process Lévy-Khintchine formula Lévy-type process Path properties Pseudo-differential operator

Authors and affiliations

  • Björn Böttcher
    • 1
  • René Schilling
    • 2
  • Jian Wang
    • 3
  1. 1.Institut für Mathematische StochastikTechnische Universität DresdenDresdenGermany
  2. 2.Institut für Mathematische StochastikTechnische Universität DresdenDresdenGermany
  3. 3.School of Mathematics and Computer ScienceFujian Normal UniversityFuzhou, FujianPeople's Republic of China

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-02684-8
  • Copyright Information Springer International Publishing Switzerland 2013
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-02683-1
  • Online ISBN 978-3-319-02684-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site