L}}vy Processes and Infinitely Divisible Distributions [Paperback]

A corrected edition of a highly successful introductory text for graduate students. Assumes no prior knowledge of stochastic processes.This successful text provides a comprehensive basic knowledge of L?vy processes and serves as an introduction to stochastic processes in general. Now in paperback, this corrected edition contains a brand new supplement discussing relevant developments in the area since the book's initial publication.This successful text provides a comprehensive basic knowledge of L?vy processes and serves as an introduction to stochastic processes in general. Now in paperback, this corrected edition contains a brand new supplement discussing relevant developments in the area since the book's initial publication.L?vy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book is intended to provide the reader with comprehensive basic knowledge of L?vy processes, and at the same time serve as an introduction to stochastic processes in general. No specialist knowledge is assumed and proofs are given in detail. Systematic study is made of stable and semi-stable processes, and the author gives special emphasis to the correspondence between L?vy processes and infinitely divisible distributions. All serious students of random phenomena will find that this book has much to offer. Now in paperback, this corrected edition contains a brand new supplement discussing relevant developments in the area since the book's initial publication.Preface to the revised edition; Remarks on notation; 1. Basic examples; 2. Characterization and existence; 3. Stable processes and their extensions; 4. The L?vyIt? decomposition of sample functions; 5. Distributional properties of L?vy processes; 6. Subordination and density transformation; 7. Recurrence and transience; 8. Potential theory for L?vy processes; 9. WienerHopf factorizations; 10. More distributional properties; Supplement; Solcå