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Operator-stable distributions and stable marginals

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  • Hudson, William N.

Abstract

Sharpe has shown that full operator-stable distributions [mu] on Rn are infinitely divisible and for a suitable automorphism B depending on [mu] satisfy the relation [mu]t = [mu]t-B * [delta](b(t)) for all t > 0. B is called an exponent for [mu]. It is proved here that if an operator-stable distribution on Rn has n linearly independent univariate stable marginals, then its exponents are semi-simple operators. In addition necessary and sufficient conditions are given for such a distribution on R2 to have univariate stable marginals. The proofs use a hitherto unpublished result of Sharpe's that all full operator-stable distributions are absolutely continuous. His proof is provided here.

Suggested Citation

  • Hudson, William N., 1980. "Operator-stable distributions and stable marginals," Journal of Multivariate Analysis, Elsevier, vol. 10(1), pages 26-37, March.
    • Handle: RePEc:eee:jmvana:v:10:y:1980:i:1:p:26-37
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    Cited by:

    1. Hudson, William N. & Veeh, Jerry Alan, 2001. "Complex Stable Sums of Complex Stable Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 77(2), pages 229-238, May.

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