Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition
Alfonso Rocha-Arteaga author Ken-iti Sato author
Format:Paperback
Publisher:Springer Nature Switzerland AG
Published:6th Nov '19
Currently unavailable, and unfortunately no date known when it will be back
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 L
The book is divided into five chapters. Chapter 1 studies basic properties of L
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 L
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.
“The text is written in good style by giving exact definitions followed by statements and their proofs. The notions and the results are well illustrated by a reasonable number of examples. … Each chapter ends with extremely useful ‘Notes’. Thus there are five well-written essays containing historical facts and going through important steps in developing the infinite divisibility and the theory of Lévy processes. All comments are supported by referring to original sources.” (Jordan M. Stoyanov, zbMATH 1472.60003, 2021)
ISBN: 9783030226992
Dimensions: unknown
Weight: unknown
135 pages
1st ed. 2019