Persistence and first-passage properties in nonequilibrium systems
In this review, we discuss the persistence and the related first-passage properties in
extended many-body nonequilibrium systems. Starting with simple systems with one or few …
extended many-body nonequilibrium systems. Starting with simple systems with one or few …
Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
Modern microscopic techniques following the stochastic motion of labelled tracer particles
have uncovered significant deviations from the laws of Brownian motion in a variety of …
have uncovered significant deviations from the laws of Brownian motion in a variety of …
Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian
process with a power-law time dependent diffusion coefficient. Its mean squared …
process with a power-law time dependent diffusion coefficient. Its mean squared …
First exit times of harmonically trapped particles: a didactic review
DS Grebenkov - Journal of Physics A: Mathematical and …, 2014 - iopscience.iop.org
We revise the classical problem of characterizing first exit times of a harmonically trapped
particle whose motion is described by a one-or multidimensional Ornstein–Uhlenbeck …
particle whose motion is described by a one-or multidimensional Ornstein–Uhlenbeck …
First passage and first hitting times of Lévy flights and Lévy walks
For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-
passage and first-hitting (or first-arrival) times. These are, respectively, the times when the …
passage and first-hitting (or first-arrival) times. These are, respectively, the times when the …
Spectral content of a single non-Brownian trajectory
Time-dependent processes are often analyzed using the power spectral density (PSD)
calculated by taking an appropriate Fourier transform of individual trajectories and finding …
calculated by taking an appropriate Fourier transform of individual trajectories and finding …
First passages in bounded domains: When is the mean first passage time meaningful?
We study the first passage statistics to adsorbing boundaries of a Brownian motion in
bounded two-dimensional domains of different shapes and configurations of the adsorbing …
bounded two-dimensional domains of different shapes and configurations of the adsorbing …
Reflected fractional Brownian motion in one and higher dimensions
Fractional Brownian motion (FBM), a non-Markovian self-similar Gaussian stochastic
process with long-ranged correlations, represents a widely applied, paradigmatic …
process with long-ranged correlations, represents a widely applied, paradigmatic …
Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-
time correlated increments and is frequently used to model anomalous diffusion processes …
time correlated increments and is frequently used to model anomalous diffusion processes …
Probability density of the fractional Langevin equation with reflecting walls
We investigate anomalous diffusion processes governed by the fractional Langevin
equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As …
equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As …