We study the tail behavior of the distribution of certain subadditive functionals acting on the sample paths of Lévy processes. The functionals we consider have, roughly speaking, the following property: only the points of the process that lie above a certain curve contribute to the value of the functional. Our assumptions will make sure that the process ends up eventually below the curve. Our results apply to ruin probabilities, distributions of sojourn times over curves, last hitting times and other functionals.
"Tail Probabilities of Subadditive Functionals of Lévy Processes." Ann. Appl. Probab. 12 (1) 69 - 100, February 2002. https://doi.org/10.1214/aoap/1015961156