Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition

Alfonso Rocha-Arteaga

ISBN 10: 3030226999 / ISBN 13: 9783030226992

Published by Springer, Springer VS, 2019

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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 ofLm 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.

Seller Inventory # 9783030226992

Bibliographic Details

• Title: Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition
• Publisher: Springer, Springer VS
• Publication Date: 2019
• Language: English
• ISBN 10: 3030226999
• ISBN 13: 9783030226992
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 9D millimeters 235 millimeters width by 155 millimeters height by 9 millimeters depth
• Weight: 230 grams

About this title

Synopsis

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,...,∞, 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 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.

 

From the Back Cover