SpringerBriefs in Probability and Mathematical Statistics

Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition

Authors: Rocha-Arteaga, Alfonso, Sato, Ken-iti

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  • Includes useful notes at the end of each chapter as historical reviews and detailed information on the used sources
  • Offers an interesting and enjoyable insight into the topics covered
  • Presents framework of the selected topics in new approach
  • Self-contained study on the relation of self-decomposable distributions with each of the selected topic
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  • ISBN 978-3-030-22700-5
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  • ISBN 978-3-030-22699-2
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About this book

This book deals with topics in the area of Lévy processes and infinitely divisible distributions such as Ornstein-Uhlenbeck type processes, selfsimilar additive processes and multivariate subordination. These topics are developed around a decreasing chain of classes of distributions Lm, m = 0,1,...,∞, from the class L0 of selfdecomposable distributions to the class L generated by stable distributions through convolution and convergence.

The book is divided into five chapters. Chapter 1 studies basic properties of Lm classes needed for the subsequent chapters.  Chapter 2 introduces Ornstein-Uhlenbeck type processes generated by a Lévy process through stochastic integrals based on Lévy processes. Necessary and sufficient conditions are given for a generating Lévy process so that the OU type process has a limit distribution of Lm class.

Chapter 3 establishes the correspondence between selfsimilar additive processes and selfdecomposable distributions and makes a close inspection of the Lamperti transformation, which transforms selfsimilar additive processes and stationary type OU processes to each other.  

Chapter 4 studies multivariate subordination of a cone-parameter Lévy process by a cone-valued Lévy process.  Finally, Chapter 5 studies strictly stable and Lm properties inherited by the subordinated process in multivariate subordination.

In this revised edition, new material is included on advances in these topics. It is rewritten as self-contained as possible. Theorems, lemmas, propositions, examples and remarks were reorganized; some were deleted and others were newly added. The historical notes at the end of each chapter were enlarged.

This book is addressed to graduate students and researchers in probability and mathematical statistics who are interested in learning more on Lévy processes and infinitely divisible distributions.

 


Table of contents (5 chapters)

Table of contents (5 chapters)
  • Classes Lm and Their Characterization

    Pages 1-26

    Rocha-Arteaga, Alfonso (et al.)

  • Classes Lm and Ornstein–Uhlenbeck Type Processes

    Pages 27-59

    Rocha-Arteaga, Alfonso (et al.)

  • Selfsimilar Additive Processes and Stationary Ornstein–Uhlenbeck Type Processes

    Pages 61-75

    Rocha-Arteaga, Alfonso (et al.)

  • Multivariate Subordination

    Pages 77-106

    Rocha-Arteaga, Alfonso (et al.)

  • Inheritance in Multivariate Subordination

    Pages 107-119

    Rocha-Arteaga, Alfonso (et al.)

Buy this book

eBook 21,39 €
39,99 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-22700-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 25,99 €
51,99 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-22699-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition
Authors
Series Title
SpringerBriefs in Probability and Mathematical Statistics
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-22700-5
DOI
10.1007/978-3-030-22700-5
Softcover ISBN
978-3-030-22699-2
Series ISSN
2365-4333
Edition Number
1
Number of Pages
VIII, 135
Additional Information
Previously published by Sociedad Matematica Mexicana, San Andrés Totoltepec, 2003
Topics