Krein's Theory applied to fluctuations of L\'{e}vy processes
  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. 
Sonia Fourati (LMI, PMA)