The big-jump principle is a well-established mathematical result for sums of independent
and identically distributed random variables extracted from a fat-tailed distribution. It states …

We consider the statistics of occupation times, the number of visits at the origin, and the
survival probability for a wide class of stochastic processes, which can be classified as …

Rare events in the first-passage distributions of jump processes are capable of triggering
anomalous reactions or series of events. Estimating their probability is particularly important …

We consider a persistent random walk on an inhomogeneous environment where the
reflection probability depends only on the distance from the origin. Such an environment is …

We consider transport properties for a non-homogeneous persistent random walk, that may
be viewed as a mean-field version of the Lévy–Lorentz gas, namely a 1D model …

Rare events in stochastic processes with heavy-tailed distributions are controlled by the big
jump principle, which states that a rare large fluctuation is produced by a single event and …

We consider a random walk $ Y $ moving on a\emph {L\'evy random medium}, namely a one-
dimensional renewal point process with inter-distances between points that are in the …

We present random walks in random sceneries as well as three related models: U-statistics
indexed by random walks, a model of stratified media with inhomogeneous layers (random …

The Lévy–Lorentz gas describes the motion of a particle on the real line in the presence of a
random array of scattering points, whose distances between neighboring points are heavy …

We study a random walk on a point process given by an ordered array of points (ω k, k∈ Z)
on the real line. The distances ω k+ 1− ω k are iid random variables in the domain of …