Introductory Lectures on Fluctuations of Lévy Processes with Applications

1. Auflage 2006
ISBN: 978-3-540-31342-7
Verlag: Springer

Buch, Englisch, 378 Seiten, PB, Format (B × H): 155 mm x 235 mm, Gewicht: 1220 g

Reihe: Universitext

This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness.

Zielgruppe

Graduate

Autoren/Hrsg.

Kyprianou, Andreas E.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

Lévy processes and applications.- The Lévy-Itô decomposition and path structure.- More distributional and path related properties.- Subordinators at first passage and renewal measures.- General storage models and paths of bounded variation.- The Wiener-Hopf factorisation.- Lévy processes at first passage and insurance risk.- Exit problems for spectrally negative processes.- Applications to optimal stopping problems. Continuous state branching processes and other applications.

Über Autor(innen)

Andreas Kyprianou has a degree in Mathematics from the University of Oxford and a Ph.D. in Probability Theory from The University of Sheffield. He is currently a Professor of Probability at the University of Bath, having held academic positions in Mathematics and Statistics Departments at the London School of Economics, Edinburgh University, Utrecht University and Heriot-Watt University, besides working for nearly two years as a research mathematician in the oil industry. His research is focused on pure and applied probability.