Nonextensive foundation of Levy distributions

A deep connection between the ubiquity of Levy distributions in nature and the nonextensive thermal statistics introduced a decade ago has been established recently [Tsallis et al, Phys. Rev. Lett. 75, 3589 (1995)], by using unnormalized q-expectation values. It has just been argued on physical grounds that normalized q-expectation values should be used instead. We revisit, within this more appropriate scheme, the Levy problem and verify that the relevant analytic results became sensibly simplified, whereas the basic physics remains unchanged. [S1063-651X(99)14008-X].