Centering problems for probability measures on finite dimensional vector spaces

Details Centering problems for probability measures on finite dimensional vector spaces Centering problems for probability measures on finite dimensional vector spaces

2010-01-12

arxiv.org/abs/1001.1963v1

Mathematics

Probability

Scientific paper

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 $\mu*\delta(h)=S(\mu*\delta (h))$ for each symmetry $S$ of $\mu$, generalizing thus Jurek's result obtained for full measures. An explicit form of the $h$ is given for infinitely divisible $\mu$. 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.

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