I think the result goes back to Polya, see <a href="http://www.ams.org/journals/tran/1960-095-02/S0002-9947-1960-0119247-6/">"Some theorems on stable processes"</a> by Blumenthal and Getoor. Another reference is Paul Levy "Sur une application de la dérivée d’ordre non entier au calcul des probabilités" page 1118 of <a href="http://gallica.bnf.fr/ark:/12148/bpt6k31295.r=comptes%20rendus%20academie%20des%20sciences%201923?rk=42918;4">CRAS 1923</a>.