Krein's Theory applied to fluctuations of L\'evy processes
Abstract
We give an interpretation of the bilateral exit problem for L\'evy processes via the study of an elementary Markov chain. We exhibit a strong connection between this problem and Krein's theory on strings. For instance, for symmetric L\'evy processes with bounded variations, the L\'evy exponent is the correspondant spectral density and the Wiener-Hopf factorization turns out to be a version of Krein's entropy formula.
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