We review recent advances on the record statistics of strongly correlated time series, whose
entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of …

The present work provides a critical assessment of numerical solutions of the space-
fractional diffusion-advection equation, which is of high significance for applications in …

We study the statistics of the number of records R n, N for N identical and independent
symmetric discrete-time random walks of n steps in one dimension, all starting at the origin …

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 …

The statistical description of a one-dimensional superdiffusive Lévy flier restricted to a finite
domain is well known to be technically involving. For example, in this type of process the …

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 …

In this paper, the absorption of a particle undergoing Lévy flight in the presence of a point
sink of arbitrary strength and position is studied. The motion of such a particle is given by a …

We consider a one-dimensional asymmetric random walk whose jumps are identical,
independent and drawn from a distribution ϕ (η) displaying asymmetric power-law tails (ie ϕ …

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 …