Taylor expansions of $R$-transforms, application to supports and moments
Florent Benaych-Georges
60E1046L5460E07R-transformfree cumulantsfree infinitely divisible distributions
We prove that a probability measure on the real line has a moment of order (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. We then 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 even order $p$, if and only if its L\'evy measure does so. We also prove a weaker version of the last result when $p$ is odd.
Indiana University Mathematics Journal
2006
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10.1512/iumj.2006.55.2691
10.1512/iumj.2006.55.2691
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Indiana Univ. Math. J. 55 (2006) 465 - 482
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