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.

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.

A systematic treatment of stable Lévy processes and self-similar Markov processes, for graduate students and researchers in the field.