Around the 1960s a celebrated collection of papers emerged offering a number of explicit
identities for the class of isotropic Lévy stable processes in one and higher dimensions; …

Stable Lévy processes lie at the intersection of Lévy processes and self-similar Markov
processes. Processes in the latter class enjoy a Lamperti-type representation as the space …

We investigate the first-passage dynamics of symmetric and asymmetric Lévy flights in semi-
infinite and bounded intervals. By solving the space-fractional diffusion equation, we …

From the point of view of stochastic analysis the Caputo and Riemann-Liouville derIvatives
of order α∈(0, 2) can be viewed as (regularized) generators of stable Lévy motions …

The fractional Laplace operator appears in various areas of pure and applied mathematics.
This survey collects several equivalent definitions of this operator, most …

For any two-sided jumping α-stable process, where 1<α<2, we find an explicit identity for the
law of the first hitting time of the origin. This complements existing work in the symmetric …

The term'Lévy flights' was coined by Benoit Mandelbrot, who thus poeticized α-stable Lévy
random motion, a Markovian process with stationary independent increments distributed …

Abstract The Lamperti–Kiu transformation for real-valued self-similar Markov processes
(rssMp) states that, associated to each rssMp via a space-time transformation, there is a …

In his seminal work from the 1950s, William Feller classified all onedimensional diffusions
on−∞≤ a< b≤∞ in terms of their ability to access the boundary (Feller's test for explosions) …

An important open problem in the theory of Lévy flights concerns the analytically tractable
formulation of absorbing boundary conditions. Although the nonlocal approach, where the …