Taylor expansions of R-transforms, application to supports and moments

Details Taylor expansions of R-transforms, application to supports and moments Taylor expansions of R-transforms, application to supports and moments

2004-10-21

arxiv.org/abs/math/0410459v3

Mathematics

Probability

to appear in Indiana University Mathematics Journal

Scientific paper

We prove that a probability measure on the real line has a moment of order p (even integer), if and only if its R-transform admits a Taylor expansion with p terms. We also prove a weaker version of this result when p is odd. Then, we apply this to prove that a probability measure whose R-transform extends analytically to a ball with center zero is compactly supported, and that a free infinitely divisible distribution has a moment of order p even, if and only if its Levy measure does so. We also prove a weaker version of the last result when p is odd.

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