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- W2023591821 abstract "We introduce a class of probability measures whose densities near infinity are mixtures of Pareto distributions. This class can be characterized by the Fourier transform which has a power series expansion including real powers, not only integer powers. This class includes stable distributions in probability and also non-commutative probability theories. We also characterize the class in terms of the Cauchy-Stieltjes transform and the Voiculescu transform. If the stability index is greater than one, stable distributions in probability theory do not belong to that class, while they do in non-commutative probability." @default.
- W2023591821 created "2016-06-24" @default.
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- W2023591821 date "2011-07-19" @default.
- W2023591821 modified "2023-10-14" @default.
- W2023591821 title "Fourier and Cauchy-Stieltjes transforms of power laws including stable distributions" @default.
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- W2023591821 doi "https://doi.org/10.48550/arxiv.1107.3874" @default.
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