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.
Categories: math.PR