Abstract
We investigate densities of vaguely continuous convolution semigroups
of probability measures on
ℝ
d
{{\mathbb{R}^{d}}}
.
First, we provide results that give upper estimates
in a situation when the corresponding jump measure is allowed to be highly non-symmetric.
Further, we prove upper estimates of the density and its derivatives if the jump measure compares
with an isotropic unimodal measure and the characteristic exponent satisfies a certain scaling condition.
Lower estimates are discussed in view of a recent development in that direction,
and in such a way to complement upper estimates.
We apply all those results to establish precise estimates of densities of non-symmetric Lévy processes.
On the Hausdorff continuity of free Lèvy processes and free convolution semigroups
