Fluctuation Theory for Levy Processes: Ecole d'Ete de Probabilites de Saint-Flour XXXV - 2005

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Levy processes, that is, processes in continuous time with stationary and independent increments, 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 they include particularly important examples having heavy tails. Their sample path behaviour poses a variety of challenging and fascinating problems, which are addressed in detail.