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Abstract
LetX,X 1,X 2,... be i.i.d. random vectors in ℝd. The limit laws μ that can arise by suitable affine normalizations of the partial sums,S n=X 1+...+X n, are calledoperator-stable laws. These laws are a natural extension to ℝ d of the stable laws onℝ. Thegeneralized domain of attraction of μ[GDOA(μ)] is comprised of all random vectorsX whose partial sums can be affinely normalized to converge to μ. If the linear part of the affine transformation is restricted to take the formn −B for some exponent operatorB naturally associated to μ thenX is in thegeneralized domain of normal attraction of μ [GDONA(μ)]. This paper extends the theory of operator-stable laws μ and their domains of attraction and normal attraction.
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