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A characterization of Lévy probability distribution functions on Euclidean spaces

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  • Wolfe, Stephen James

Abstract

In 1937, Paul Lévy proved two theorems that characterize one-dimensional distribution functions of class L. In 1972, Urbanik generalized Lévy's first theorem. In this note, we generalize Lévy's second theorem and obtain a new characterization of Lévy probability distribution functions on Euclidean spaces. This result is used to obtain a new characterization of operator stable distribution functions on Euclidean spaces and to show that symmetric Lévy distribution functions on Euclidean spaces need not be symmetric unimodal.

Suggested Citation

  • Wolfe, Stephen James, 1980. "A characterization of Lévy probability distribution functions on Euclidean spaces," Journal of Multivariate Analysis, Elsevier, vol. 10(3), pages 379-384, September.
    • Handle: RePEc:eee:jmvana:v:10:y:1980:i:3:p:379-384
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