Dual Lukacs regressions for non-commutative variables
Kamil Szpojankowski , Jacek Wesołowski
AbstractDual Lukacs type characterizations of random variables in free probability are studied here. First, we develop a freeness property satisfied by Lukacs type transformations of free-Poisson and free-Binomial non-commutative variables which are free. Second, we give a characterization of non-commutative free-Poisson and free-Binomial variables by properties of first two conditional moments, which mimic Lukacs type assumptions known from classical probability. More precisely, our result is a non-commutative version of the following result known in classical probability: if \$U\$, \$V\$ are independent real random variables, such that \$E(V(1-U)\\textbar\UV)\$ and \$E(V\\textasciicircum\2(1-U)\\textasciicircum\2\\textbar\UV)\$ are non-random then \$V\$ has a gamma distribution and \$U\$ has a beta distribution.
|Journal series||arXiv:1110.3419, (0 pkt)|
|Keywords in English||46L54 (Primary), 62E10 (Secondary), Mathematics - Operator Algebras, Mathematics - Probability|
|Citation count*||1 (2013-01-30)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.