We investigate densities of vaguely continuous convolution semigroups of probability
measures on ℝ d. First, we provide results that give upper estimates in a situation when the …

A stable-like process is a Feller process $(X_t) _ {t\geq 0} $ taking values in $\mathbb {R}^ d
$ and whose generator behaves, locally, like an $\alpha $-stable L\'evy process, but the …

A maximal inequality is an inequality which involves the (absolute) supremum sup s⩽ t| X s|
or the running maximum sup s⩽ t X s of a stochastic process (X t) t⩾ 0. We discuss maximal …

We study a time-inhomogeneous SDE in $\mathbb {R}^ d $ driven by a cylindrical Lévy
process with independent coordinates which may have different scaling properties. Such a …

We consider non-local Schrödinger operators H=-LV in L 2 (R d), d⩾ 1, where the kinetic
terms L are pseudo-differential operators which are perturbations of the fractional Laplacian …

We prove the existence and asymptotic behaviour of the transition density for a large class of
subordinators whose Laplace exponents satisfy lower scaling condition at infinity …

We prove the existence and give estimates of the fundamental solution (the heat kernel) for
the equation $\partial_t=\mathcal {L}^{\kappa} $ for non-symmetric non-local operators …

We prove universality of the Yaglom limit of Lipschitz cones among all unimodal Lévy
processes sufficiently close to the isotropic α-stable Lévy process. Résumé. On prouve …

We present a general approach to the parametrix construction. We apply it to prove the
uniqueness and existence of a weak fundamental solution for the equation∂ tu= L u …

In this paper, we discuss estimates on the transition densities of subordinators, which are
global in time. We establish sharp two-sided estimates on the transition densities of …