On the Extreme-Value Theory for Stationary Diffusions Under Power Normalization

We consider regular positive recurrent diffusion processes on an open interval (l,r) R¹ with inaccessible end points. Necessary and sufficient conditions are given in terms of the scale functions describing the domains of attraction of the nondegenerate limiting probability laws for the extreme-values under power normalization. Sufficient von Mises-type conditions and formulas for norming constants are also obtained.