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 …

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 …

Systems driven by α-stable noises could be very different from their Gaussian counterparts.
Stationary states in single-well potentials can be multimodal. Moreover, a potential well …

We revisit the problem of calculating the survival probability of Lévy flights in a finite interval
with absorbing boundaries. Our approach is based on the master equation for discrete Lévy …

We study the large-time asymptotic of renewal-reward processes with a heavy-tailed waiting
time distribution. It is known that the heavy tail of the distribution produces an extremely slow …

In this paper we provide an analysis of a mean first passage time problem of a random
walker subject to a bivariate α-stable Lévy-type noise from a 2-dimensional disk. For an …

The big jump principle explains the emergence of extreme events for physical quantities
modelled by a sum of independent and identically distributed random variables which are …

The concept of transport mediated through the dynamics of “jumping” particles is used to
develop an iterative method for obtaining steady-state solutions to the nonlocal transport …

We consider a one-dimensional continuous time random walk (CTRW) on a fixed time
interval T where at each time step the walker waits a random time τ, before performing a …

We establish an exact formula relating the survival probability for certain L\'evy flights (viz.
asymmetric $\alpha $-stable processes where $\alpha= 1/2$) with the survival probability for …