Consider the following stochastic differential equation (SDE) d X t= b (t, X t−) d t+ d L t, X 0=
x, driven by a d-dimensional Lévy process (L t) t≥ 0. We establish conditions on the Lévy …

Estimates of transition densities and their derivatives for jump Lévy processes - ScienceDirect
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We derive explicitly the coupling property for the transition semigroup of a Lévy process and
gradient estimates for the associated semigroup of transition operators. This is based on the …

Dirichlet heat kernel for unimodal Lévy processes - ScienceDirect Skip to main contentSkip
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In this note, we study the integrodifferential operator (I− Δ) log corresponding to the
logarithmic symbol log⁡(1+| ξ| 2), which is a singular integral operator given by (I− Δ) log u …

Due to the increasing power of modern computers, it has become ever more popular to use
sophisticated models to describe the irregular behaviour of real life phenomena. Nowadays …

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 …

We construct the fundamental solution (the heat kernel) p κ to the equation∂ t= L κ, where
under certain assumptions the operator L κ takes one of the following forms, L κ f (x):=∫ R d …

These lecture notes are an extended version of my lectures on Lévy and Lévy-type
processes given at the Second Barcelona Summer School on Stochastic Analysis organized …

We introduce a class of Lévy processes subject to specific regularity conditions, and
consider their Feynman–Kac semigroups given under a Kato-class potential. Using new …