# On a Method of Introducing Free-Infinitely Divisible Probability Measures

@article{Jurek2014OnAM,
title={On a Method of Introducing Free-Infinitely Divisible Probability Measures},
author={Zbigniew J. Jurek},
journal={Demonstratio Mathematica},
year={2014},
volume={49},
pages={236 - 251}
}
• Z. Jurek
• Published 15 December 2014
• Mathematics
• Demonstratio Mathematica
Abstract Random integral mappings give isomorphism between the subsemigroups of the classical (I D, *) and the free-infinite divisible (I D, ⊞) probability measures. This allows us to introduce new examples of such measures, more precisely their corresponding characteristic functionals.
3 Citations
We study two ways (levels) of finding free-probability analogues of classical infinitely divisible measures. More precisely, we identify their Voiculescu transforms. For free-selfdecomposable
We show that a function $\tan(1/it)$ is a Pick function (free-infinitely divisible transform) and indicate its connections with a probability. Moreover, we found its "counterpart" in classical
For the class of free-infinitely divisible transforms are introduced three families of increasing Urbanik type subclasses of those transforms. They begin with the class of free-normal transforms and

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In [Z.J. Jurek, Relations between the s-selfdecomposable and selfdecomposable measures, Ann. Probab., 13(2):592–608, 1985] and [Z.J. Jurek, Random integral representation for classes of limit