Fluctuation Theory for Lévy Processes - Ecole d'Eté de Probabilités de Saint-Flour XXXV - 2005

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.

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.

Zusammenfassung

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.

Produktdetails

• Autoren: Ronald A Doney, Ronald A. Doney
• Mitarbeit: Jea Picard (Herausgeber), Jean Picard (Herausgeber)
• Verlag: Springer, Berlin
• Sprache: Englisch
• Produktform: Taschenbuch
• Erschienen: 23.02.2011
• EAN: 9783540485100
• ISBN: 978-3-540-48510-0
• Seiten: 155
• Abmessung: 158 mm x 232 mm x 11 mm
• Gewicht: 454 g
• Illustration: IX, 155 p.
• Serien: Lecture Notes in Mathematics; École d'Été de Probabilités de Saint-Flour; Lecture Notes in Mathematics; École d'Été de Probabilités de Saint-Flour
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Stochastik, B, Mathematics and Statistics, Probability Theory and Stochastic Processes, Probabilities, Stochastics, Probability Theory, local time, Wiener-Hopf factorisation