Author Description

<p>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 <i>Lm</i>, m = 0,1,...,∞, from the class <i>L0</i> of selfdecomposable distributions to the class <i>L</i><i>∞</i> generated by stable distributions through convolution and convergence.</p><p>The book is divided into five chapters. Chapter 1 studies basic properties of <i>Lm </i>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 <i>Lm</i> class.</p><p>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. <br></p><p>Chapter 4 studies multivariate subordination of a cone-parameter Lévy process by a cone-valued Lévy process. Finally, Chapter 5 studies strictly stable and <i>Lm</i> properties inherited by the subordinated process in multivariate subordination.<br></p><p>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.<br></p><p>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.</p><p> </p><p> </p><br><p></p>