Lévy Processes and Infinitely Divisible Distributions

This book provides the reader with comprehensive basic knowledge of Lévy processes.

Ken-iti Sato (Author)

9780521553025, Cambridge University Press

Hardback, published 11 November 1999

500 pages
23.7 x 15.8 x 3.2 cm, 0.805 kg

'… an important monograph which should find a place on the bookshelf of any practising probabilist.' David Applebaum, Mathematical Gazette

Lévy 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 Lévy 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 Lévy 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 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.

Subject Areas: Calculus & mathematical analysis [PBK]