ON FREE INFINITE DIVISIBILITY FOR CLASSICAL MEIXNER
DISTRIBUTIONS
Marek Bożejko
Takahiro Hasebe
Abstract: We prove that symmetric Meixner distributions, whose probability densities are
proportional to
, are freely infinitely divisible for
. The case
corresponds to the law of Lévy’s stochastic area whose probability density is
. A
logistic distribution, whose probability density is proportional to
, is also freely
infinitely divisible.
2000 AMS Mathematics Subject Classification: Primary: 46L54; Secondary:
30C45.
Keywords and phrases: Meixner distribution, Lévy’s stochastic area, logistic
distribution, free infinite divisibility.