Barriers, exit time and survival probability for unimodal Lévy processes | Probability Theory
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The fractional Laplacian (− Δ) α/2, α∈(0, 2), has many equivalent (albeit formally different)
realizations as a nonlocal generator of a family of α-stable stochastic processes in R n. On …

For $ d\geq1 $ and $0<\beta<\alpha< 2$, consider a family of pseudo differential operators
$\{\Delta^{\alpha}+ a^\beta\Delta^{\beta/2} $; $ a\in [0, 1]\} $ on $\mathbb {R}^ d $ that …

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 this article we investigate the semilinear stochastic partial differential equation du (t, x)=(Δ
u (t, x)+ γ u (t, x)+ G (u (t, x))) d t+ κ u (t, x) d Z t on a smooth domain D⊂ R d, with Dirichlet …

We study two properties of semigroups of sub-Markov kernels, namely uniform conditional
ergodicity and intrinsic ultracontractivity. In this paper we investigate the relationship …

Suppose that $ Y_t $ is a $ d $-dimensional symmetric Lévy process such that its Lévy
measure differs from the Lévy measure of the isotropic $\alpha $-stable process ($0<\alpha< …

We address L\'{e} vy-stable stochastic processes in bounded domains, with a focus on a
discrimination between inequivalent proposals for what a boundary data-respecting …

Abstract For any α∈(0, 2), a truncated symmetric α-stable process in ℝ d is a symmetric Lévy
process in ℝ d with no diffusion part and with a Lévy density given by c| x|− d− α 1 {| x|< 1} for …