Levy 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 Levy 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 Levy processes and infinitely divisible distributions. All serious students of random phenomena will find that this book has much to offer.
Preface; Remarks on notation; 1. Basic examples; 2. Characterization and existence of Levy and additive processes; 3. Stable processes and their extensions; 4. The Levy-Ito decomposition of sample functions; 5. Distributional properties of Levy processes; 6. Subordination and density transformation; 7. Recurrence and transience; 8. Potential theory for Levy processes; 9. Wiener-Hopf factorizations; 10. More distributional properties; Solutions to exercises; References and author index; Subject index.