On the stability of one characterization of the stable distributions - Yanushkevichiene, Olga; Yanushkevichius, Romanas (Lietuvos matematikos rinkinys, 2001)
As early as 1923, Georg P6lya wrote: ``The Gaussian error law possesses the property that it remains valid under a linear combination of errors. The Gaussian error law can be characterized by this property to some extent – it is the only law that admits steadiness with respect to linear combinations of errors’’. The idea of using linear combinations of random variables to characterize the stable distributions has been extended by P. Levy. We investigate the stability of this characterization.