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Exponents and Symmetry of Operator Lévy's Probability Measures on Finite Dimensional Vector Spaces

Author

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  • Andrzej Łuczak

    (Łódź University)

Abstract

We show that for a full operator Lévy's measure on a finite dimensional vector space there exists an exponent with suitable spectral properties commuting with the symmetry group of the measure. Such exponents lead to a simple description of the symmetry group, and allow one to obtain new (commuting or not) exponents; moreover, for them a simple relation exists between the symmetry group of the operator Lévy's measure and the symmetry group of the mixing measure. We also show that full operator Lźvy's measures having “large” symmetry group need not be multivariate Lévy's, correcting some earlier result.(2)

Suggested Citation

  • Andrzej Łuczak, 1997. "Exponents and Symmetry of Operator Lévy's Probability Measures on Finite Dimensional Vector Spaces," Journal of Theoretical Probability, Springer, vol. 10(1), pages 117-129, January.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:1:d:10.1023_a:1022646415737
    DOI: 10.1023/A:1022646415737
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