Doney / Picard Fluctuation Theory for Lévy Processes

Ecole d'Eté de Probabilités de Saint-Flour XXXV - 2005
2007
ISBN: 978-3-540-48511-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 155 Seiten, eBook

Reihe: École d'Été de Probabilités de Saint-Flour

Lévy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul Lévy, who made the connection with infinitely divisible distributions and described their structure. They form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, ... and of course finance, where the feature that they include examples having "heavy tails" is particularly important. Their sample path behaviour poses a variety of difficult and fascinating problems. Such problems, and also some related distributional problems, are addressed in detail in these notes that reflect the content of the course given by R. Doney in St. Flour in 2005.

Zielgruppe

Research

Autoren/Hrsg.

Doney, Ronald A.

Picard, Jean

Inhaltsverzeichnis

to Lévy Processes.- Subordinators.- Local Times and Excursions.- Ladder Processes and the Wiener–Hopf Factorisation.- Further Wiener–Hopf Developments.- Creeping and Related Questions.- Spitzer's Condition.- Lévy Processes Conditioned to Stay Positive.- Spectrally Negative Lévy Processes.- Small-Time Behaviour.