Fluctuation Theory for LȨvy Processes [electronic resource] : Ecole d'EtȨ de ProbabilitȨs de Saint-Flour XXXV - 2005 / by Ronald A. Doney ; edited by Jean Picard.

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

LȨvy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul LȨvy, 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.

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