Fluctuation Theory for Levy Processes Ecole D'etede Probabilites De Saint-flour 35 - 2005

L?vy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul L?vy, 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.Doney, Ronald A. is the author of 'Fluctuation Theory for Levy Processes Ecole D'etede Probabilites De Saint-flour 35 - 2005', published 2007 under ISBN 9783540485100 and ISBN 3540485104.