03918nam 22004935 450 991036085370332120250609112120.03-030-22700-610.1007/978-3-030-22700-5(CKB)4100000009759228(DE-He213)978-3-030-22700-5(MiAaPQ)EBC5997318(PPN)258870605(MiAaPQ)EBC5997224(EXLCZ)99410000000975922820191101d2019 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierTopics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition /by Alfonso Rocha-Arteaga, Ken-iti Sato1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (VIII, 135 p.) SpringerBriefs in Probability and Mathematical Statistics,2365-43333-030-22699-9 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.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. .SpringerBriefs in Probability and Mathematical Statistics,2365-4333ProbabilitiesProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Probabilities.Probability Theory and Stochastic Processes.519.2Rocha-Arteaga Alfonsoauthttp://id.loc.gov/vocabulary/relators/aut781814Sato Ken-itiauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910360853703321Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition2500664UNINA