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 …

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 …

We consider the system of stochastic differential equation $ dX_t= A (X_ {t-})\, dZ_t $, $ X_0=
x $, driven by cylindrical $\alpha $-stable process $ Z_t $ in $\mathbb {R}^ d $. We assume …

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 …

Let α (x) be a measurable function taking values in [α 1, α 2] for 0< α 1⩽ α 2< 2, and κ (x, z)
be a positive measurable function that is symmetric in z and bounded between two positive …

We consider the stochastic differential equation d X t= A (X t−) d Z t, X 0= x, driven by
cylindrical α-stable process Z t in, where α∈(0, 1) and d≥ 2. We assume that the …

We study the stochastic differential equation d X t= A (X t−) d Z t, X 0= x, where Z t=(Z t (1),…,
Z t (d)) T and Z t (1),…, Z t (d) are independent one-dimensional Lévy processes with …

In this note we prove some sufficient conditions for transience and recurrence of a Lévy-type
process in $\mathbb {R} $, whose generator defined on the test functions is of the form\begin …

Parametrix methods for equations with fractional Laplacians Page 1 Victoria P. Knopova,
Anatoly N. Kochubei, and Alexei M. Kulik Parametrix methods for equations with fractional …