Ronald A. Doney, Jean Picard (editor)3540485104, 9783540485100, 9783540485117
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. |
Table of contents :
Front Matter….Pages I-IX
Introduction to Lévy Processes….Pages 1-8
Subordinators….Pages 9-17
Local Times and Excursions….Pages 19-24
Ladder Processes and the Wiener–Hopf Factorisation….Pages 25-40
Further Wiener–Hopf Developments….Pages 41-50
Creeping and Related Questions….Pages 51-64
Spitzer’s Condition….Pages 65-80
Lévy Processes Conditioned to Stay Positive….Pages 81-93
Spectrally Negative Lévy Processes….Pages 95-113
Small-Time Behaviour….Pages 115-132
Back Matter….Pages 133-150 |
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