Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book provides the reader with comprehensive basic knowledge of Lévy processes, and at the same time introduces stochastic processes in general. No specialist knowledge is assumed and proofs and exercises are given in detail. The author systematically studies stable and semi-stable processes and emphasizes the correspondence between Lévy processes and infinitely divisible distributions. All serious students of random phenomena will benefit from this volume.
Contents
Preface; Remarks on notation; 1. Basic examples; 2. Characterization and existence of Lévy and additive processes; 3. Stable processes and their extensions; 4. The Lévy-Itô decomposition of sample functions; 5. Distributional properties of Lévy processes; 6. Subordination and density transformation; 7. Recurrence and transience; 8. Potential theory for Lévy processes; 9. Wiener-Hopf factorizations; 10. More distributional properties; Solutions to exercises; References and author index; Subject index.
Review
"This book is a work of scrupulous scholarship, and an impressively detailed compendium of knowledge." Mathematical Reviews
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