Krein’s theory on strings applied to fluctuations of Lévy processes
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چکیده
LMI de l’INSA de Rouen, place Emile Blondel, 76130 Mont St Aignan. France LPMA des Universités Paris VI et VII, 4 Place Jussieu, case 188, 75252 Paris, Cedex 05. France ABSTRACT We give an interpretation of the bilateral exit problem for Lévy 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 Lévy processes with bounded variations, the Lévy 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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تاریخ انتشار 2008