Centering Problems for Probability Measures on Finite-Dimensional Vector Spaces

Andrzej Łuczak ()
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Andrzej Łuczak: Łódź University

Journal of Theoretical Probability, 2010, vol. 23, issue 3, 770-791

Abstract: 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.

Keywords: Centering probability measures; Infinitely divisible laws; Quasi-decomposable (operator-semistable and operator-stable) laws; 60E07; 60B11 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-010-0294-7

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