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Centering Problems for Probability Measures on Finite-Dimensional Vector Spaces

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  • Andrzej Łuczak

    (Łódź University)

Abstract

The paper deals with various centering problems for probability measures on finite-dimensional vector spaces. We show that for every such measure, there exists a vector h satisfying μ δ(h)=S(μ δ(h)) for each symmetry S of μ, generalizing thus Jurek’s result obtained for full measures. An explicit form of the h is given for infinitely divisible μ. The main result of the paper consists in the analysis of quasi-decomposable (operator-semistable and operator-stable) measures and finding conditions for the existence of a “universal centering” of such a measure to a strictly quasi-decomposable one.

Suggested Citation

  • Andrzej Łuczak, 2010. "Centering Problems for Probability Measures on Finite-Dimensional Vector Spaces," Journal of Theoretical Probability, Springer, vol. 23(3), pages 770-791, September.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:3:d:10.1007_s10959-010-0294-7
    DOI: 10.1007/s10959-010-0294-7
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    References listed on IDEAS

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    1. Hudson, William N. & Mason, J. David, 1981. "Operator-stable laws," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 434-447, September.
    2. Sato, Ken-iti, 1987. "Strictly operator-stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 22(2), pages 278-295, August.
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