Stable Lévy Processes via Lamperti-Type Representations

Andreas E. Kyprianou was educated at the University of Oxford and University of Sheffield and is currently a professor of mathematics at the University of Bath. He has spent over 25 years working on the theory and application of path-discontinuous stochastic processes and has over 130 publications, including a celebrated graduate textbook on Lévy processes. During his time in Bath, he co-founded and directed the Prob-L@B (Probability Laboratory at Bath), was PI for a multi-million-pound EPSRC Centre for Doctoral Training, and is currently the Director of the Bath Institute for Mathematical Innovation. Juan Carlos Pardo is a full professor at the department of Probability and Statistics at Centro de Investigación en Matemáticas (CIMAT). He was educated at the Universidad Nacional Autónoma de México (UNAM) and Université de Paris VI (Sorbonne Université). He has spent over 13 years working on the theory and application of path-discontinuous stochastic processes and has more than 50 publications in these areas. During the academic year 2018-2019, he held the David Parkin visiting professorship at the University of Bath.

1. Stable distributions; 2. Lévy processes; 3. Stable processes; 4. Hypergeometric Lévy processes; 5. Positive self-similar Markov processes; 6. Spatial fluctuations in one dimension; 7. Doney–Kuznetsov factorisation and the maximum; 8. Asymptotic behaviour for stable processes; 9. Envelopes of positive self-similar Markov processes; 10. Asymptotic behaviour for path transformations; 11. Markov additive and self-similar Markov processes; 12. Stable processes as self-similar Markov processes; 13. Radial reflection and the deep factorisation; 14. Spatial fluctuations and the unit sphere; 15. Applications of radial excursion theory; 16. Windings and up-crossings of stable processes; Appendix.