The Matsumoto-Yor property in free probability via subordination and Boolean cumulants
Marcin \'Swieca
TL;DR
This paper explores the Matsumoto-Yor property within free probability, establishing new characterizations of free-GIG and free Poisson distributions using subordination, Boolean cumulants, and conditional moments.
Contribution
It introduces novel characterizations of free-GIG and free Poisson distributions via freeness and conditional moments, linking subordination functions with Boolean cumulants.
Findings
New characterization of free-GIG and free Poisson distributions
Established a connection between subordination functions and Boolean cumulants
Enhanced understanding of the Matsumoto-Yor property in free probability
Abstract
We study the Matsumoto-Yor property in free probability. We prove three characterizations of free-GIG and free Poisson distributions by freeness properties together with some assumptions about conditional moments. Our main tools are subordination and Boolean cumulants. In particular, we establish a new connection between additive subordination function and Boolean cumulants.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Analytic and geometric function theory