{"product_id":"9783030226992","title":"SpringerBriefs in Probability and Mathematical Statistics","description":"\u003ch1\u003eSpringerBriefs in Probability and Mathematical Statistics\u003c\/h1\u003e \u003ch2\u003eRocha-Arteaga, Alfonso; Sato, Ken-iti\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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 \u003ci\u003eL\u003csub\u003em\u003c\/sub\u003e\u003c\/i\u003e, m = 0,1,...,∞, from the class \u003ci\u003eL\u003csub\u003e0\u003c\/sub\u003e\u003c\/i\u003e of selfdecomposable distributions to the class \u003ci\u003eL\u003c\/i\u003e\u003ci\u003e\u003csub\u003e∞\u003c\/sub\u003e\u003c\/i\u003e generated by stable distributions through convolution and convergence.\u003c\/p\u003e\u003cp\u003eThe book is divided into five chapters. Chapter 1 studies basic properties of \u003ci\u003eL\u003csub\u003em\u003c\/sub\u003e \u003c\/i\u003eclasses 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 \u003ci\u003eL\u003csub\u003em\u003c\/sub\u003e\u003c\/i\u003e class.\u003c\/p\u003e\u003cp\u003eChapter 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.  \u003cbr\u003e\u003c\/p\u003e\u003cp\u003eChapter 4 studies multivariate subordination of a cone-parameter Lévy process by a cone-valued Lévy process.  Finally, Chapter 5 studies strictly stable and \u003ci\u003eL\u003csub\u003em\u003c\/sub\u003e\u003c\/i\u003e properties inherited by the subordinated process in multivariate subordination.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eIn 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.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2019-11-06\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030226992\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-22700-5\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 135\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":46547939098764,"sku":"9783030226992","price":58.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030226992.jpg?v=1775962894","url":"https:\/\/lateknightbooks.com\/products\/9783030226992","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}