Alfonso Rocha-Arteaga, Ken-Iti Sato

Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition (eBook, PDF)

• Format: PDF

Produktbeschreibung

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_m, m = 0,1,...,8, from the class L₀ of selfdecomposable distributions to the class L₈ generated by stable distributions through convolution and convergence.

The book is divided into five chapters. Chapter 1 studies basic properties of L_m 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 L_m 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 L_m 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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 135
• Erscheinungstermin: 2. November 2019
• Englisch
• ISBN-13: 9783030227005
• Artikelnr.: 58049747

Inhaltsangabe

Classes Lm and their Characterization.- Classes Lm and Ornstein-Uhlenbeck Type Processes.- Classes Lm and Selfsimilar Additive Processes.- Multivariate Subordination.- Inheritance of Selfdecomposability in Subordination.

Rezensionen

"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)