We study the asymptotics of Dirichlet eigenvalues and eigenfunctions of the fractional
Laplacian (-Δ) s in bounded open Lipschitz sets in the small order limit s→ 0+. While it is …

Barriers, exit time and survival probability for unimodal Lévy processes | Probability Theory
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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 …

In this paper, we consider subordinate Brownian motion X in R^d, d≥1, where the Laplace
exponent ϕ of the corresponding subordinator satisfies some mild conditions. The scale …

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 …

In the first part of this article, we prove two-sided estimates of hitting probabilities of balls, the
potential kernel and the Green function for a ball for general isotropic unimodal Lévy …

In this note, we deal with the fractional logarithmic Schrödinger operator (I+(-Δ) s) log and
the corresponding energy spaces for variational study. The fractional (relativistic) logarithmic …

We are interested in the differential equations satisfied by the density of the Geometric
Stable processes G_α^β=\left{G_α^β(t);t≧0\right\}, with stability\index α∈(0,2 and symmetry …

For one-dimensional symmetric Lévy processes, which hit every point with positive
probability, we give sharp bounds for the tail function P x (TB> t), where TB is the first hitting …