返回Google圖書搜尋

Stable Lévy Processes via Lamperti-Type Representations

出版	Cambridge University Press, 2022-04-07
主題	Mathematics / GeneralMathematics / Probability & Statistics / General
ISBN	11084802929781108480291
URL	http://books.google.com.hk/books?id=0BNkEAAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋"Preface There have been a number of developments in the theory of alpha-stable Levy processes in recent years. This is largely thanks to a better understanding of their connection to self-similar Markov processes, in conjunction with a revised view on the complex analysis that can subsequently be brought into play. We mention in this respect the paper of Caballero and Chaumont [43] as well as the work of Kuznetsov [115, 116], both of which present seminal perspectives in terms of the underlying Wiener-Hopf theory that has stimulated a large base of literature. Among this literature, the PhD theses of AlexWatson in 2013 and Weerapat Satitkanitkul in 2018 stand out. The basic idea of this book is to give an introductory account of these developments and, accordingly, expose the new techniques that have appeared in the literature since the mid 2000s. The majority of the mathematical computations that are developed in the following chapters either pertain to recent material or to a new approach for classical results. At the end of each chapter, a section is devoted to referencing all material presented in the main body of the chapter. An Appendix is also included, and referred to throughout the text, to record some of the more specialist facts from complex analysis and the theory of Markov processes that are used in the text. We hope that this text will serve as a standard reference for those interested in the modern theory of alpha-stable Levy processes as well as suitable material for a graduate course. Indeed, some of the material in this text has been used in conjunction with lectures given by AEK at the University of Zurich, the National Technical University of Athens, University of Jyvaskyla, The Chinese Academy of Sciences and at Prob-L@B in Bath, as well as by JCP at UNAM in Mexico City, CIMAT in Guanajuato and Kyoto University"--