Andreas E. Kyprianou

Stable Lévy Processes via Lamperti-Type Representations (eBook, PDF)

• Format: PDF

Produktbeschreibung

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

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 31. März 2022
• Englisch
• ISBN-13: 9781108572163
• Artikelnr.: 66178458

Autorenporträt

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.

Inhaltsangabe

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.