LEADER 03918nam 22004935 450 001 9910360853703321 005 20250609112120.0 010 $a3-030-22700-6 024 7 $a10.1007/978-3-030-22700-5 035 $a(CKB)4100000009759228 035 $a(DE-He213)978-3-030-22700-5 035 $a(MiAaPQ)EBC5997318 035 $a(PPN)258870605 035 $a(MiAaPQ)EBC5997224 035 $a(EXLCZ)994100000009759228 100 $a20191101d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTopics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition /$fby Alfonso Rocha-Arteaga, Ken-iti Sato 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (VIII, 135 p.) 225 1 $aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333 311 08$a3-030-22699-9 327 $aClasses Lm and their Characterization -- Classes Lm and Ornstein-Uhlenbeck Type Processes -- Classes Lm and Selfsimilar Additive Processes -- Multivariate Subordination -- Inheritance of Selfdecomposability in Subordination. 330 $aThis book deals with topics in the area of Lévy processes and infinitely divisible distributions such as Ornstein-Uhlenbeck type processes, selfsimilar additive processes and multivariate subordination. These topics are developed around a decreasing chain of classes of distributions Lm, m = 0,1,...,?, from the class L0 of selfdecomposable distributions to the class L? generated by stable distributions through convolution and convergence. The book is divided into five chapters. Chapter 1 studies basic properties of Lm classes needed for the subsequent chapters. Chapter 2 introduces Ornstein-Uhlenbeck type processes generated by a Lévy process through stochastic integrals based on Lévy processes. Necessary and sufficient conditions are given for a generating Lévy process so that the OU type process has a limit distribution of Lm class. Chapter 3 establishes the correspondence between selfsimilar additive processes and selfdecomposable distributions and makes a close inspection of the Lamperti transformation, which transforms selfsimilar additive processes and stationary type OU processes to each other. Chapter 4 studies multivariate subordination of a cone-parameter Lévy process by a cone-valued Lévy process. Finally, Chapter 5 studies strictly stable and Lm properties inherited by the subordinated process in multivariate subordination. In this revised edition, new material is included on advances in these topics. It is rewritten as self-contained as possible. Theorems, lemmas, propositions, examples and remarks were reorganized; some were deleted and others were newly added. The historical notes at the end of each chapter were enlarged. This book is addressed to graduate students and researchers in probability and mathematical statistics who are interested in learning more on Lévy processes and infinitely divisible distributions. . 410 0$aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333 606 $aProbabilities 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aProbabilities. 615 14$aProbability Theory and Stochastic Processes. 676 $a519.2 700 $aRocha-Arteaga$b Alfonso$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781814 702 $aSato$b Ken-iti$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910360853703321 996 $aTopics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition$92500664 997 $aUNINA