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Alternative conditions for attraction to stable vectors

de Haan L., Li D., Peng L., Iglesias-Pereira H.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 2

303--317

Relying on Geluk and de Haan [3] we derive alternative necessary and sufficient conditions for the domain of attraction of a stable distribution in Rd which are phrased entirely in terms of (joint distributions of) linear combinations of the marginals. The conditions in terms of characteristic functions should be useful for determining rates of convergence, as in de Haan and Peng [4].