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arXiv · 1504.04736

Convolution, subordination and characterization problems in noncommutative probability

Wiktor Ejsmont·Uwe Franz·Kamil Szpojankowski
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Abstract

Characterization problems in free probability are studied here. Using subordination of free additive and free multiplicative convolutions we generalize some known characterizations in free probability to random variables with unbounded support. Using this technique we also prove a new characterization of distributions of free random variables. A similar technique is used to study Laha-Lukacs regressions for monotonically independent random variables.

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Wiktor Ejsmont, Uwe Franz, Kamil Szpojankowski. 2015-04-18. Convolution, subordination and characterization problems in noncommutative probability. https://doi.org/10.1512/iumj.2017.66.5971

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