Authors:
- 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
Part of the book series: SpringerBriefs in Probability and Mathematical Statistics (SBPMS)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
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.
Keywords
Reviews
Authors and Affiliations
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Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Sinaloa, Culiacán, Mexico
Alfonso Rocha-Arteaga
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Hachiman-yama 1101-5-103, Tenpaku-ku, Nagoya, Japan
Ken-iti Sato
Bibliographic Information
Book Title: Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition
Authors: Alfonso Rocha-Arteaga, Ken-iti Sato
Series Title: SpringerBriefs in Probability and Mathematical Statistics
DOI: https://doi.org/10.1007/978-3-030-22700-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-22699-2Published: 06 November 2019
eBook ISBN: 978-3-030-22700-5Published: 02 November 2019
Series ISSN: 2365-4333
Series E-ISSN: 2365-4341
Edition Number: 1
Number of Pages: VIII, 135
Additional Information: Previously published by Sociedad Matematica Mexicana, San Andrés Totoltepec, 2003