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 …

We propose using Lévy α-stable distributions to construct priors for Bayesian inverse
problems. The construction is based on Markov fields with stable-distributed increments …

The variable-order fractional Laplacian plays an important role in the study of
heterogeneous systems. In this paper, we propose the first numerical methods for the …

Using probabilistic methods we study the existence of viscosity solutions to non-linear
integro-differential equations $$\partial_t u (t, x)-\sup_ {\alpha\in I}\bigg (b_ {\alpha}(x)\cdot …

In this paper we study the domain of the generator of stable processes, stable-like processes
and more general pseudo-and integro-differential operators which naturally arise both in …

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 …

Let A be a pseudo-differential operator with negative definite symbol q. In this paper we
establish a sufficient condition such that the well-posedness of the (A,C_c^∞(R^d)) …

We present an existence result for Lévy‐type processes which requires only weak regularity
assumptions on the symbol with respect to the space variable x. Applications range from …

We characterize the local smoothness and the asymptotic growth rate of the Lévy white
noise. We do so by characterizing the weighted Besov spaces in which it is located. We …