Krein's Theory applied to fluctuations of Lévy processes

Details Krein's Theory applied to fluctuations of Lévy processes Krein's Theory applied to fluctuations of Lévy processes

2005-08-30

arxiv.org/abs/math/0508612v1

Mathematics

Probability

Scientific paper

We give an interpretation of the bilateral exit problem for L\'{e}vy 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\'{e}vy processes with bounded variations, the L\'{e}vy 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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