Related papers: Random Flights and Anomalous Diffusion: A Non-Mark…
We propose a model of sub-diffusion in which an external force is acting on a particle at all times not only at the moment of jump. The implication of this assumption is the dependence of the random trapping time on the force with the…
We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact…
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…
We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…
We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian and show…
In this work, the motion of a dust particle under the influence of the random force due to dust charge fluctuations is considered as a non-Markovian stochastic process. Memory effects in the velocity process of the dust particle are…
The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained…
Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…
We explore the diffusion process in the non-Markovian spatio-temporal noise.%the escape rate problem in the non-Markovian spatio-temporal random noise. There is a non-trivial short memory regime, i.e., the Markovian limit characterized by a…
We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical N-body hamiltonian system with long-range interaction showing a second-order phase-transition in the canonical ensemble. Anomalous…
The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail is reexamined from a fundamental statistical point of view making use of the division of particle orbits into waiting…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
We prove a superdiffusive central limit theorem for the displacement of a test particle in the periodic Lorentz gas in the limit of large times $t$ and low scatterer densities (Boltzmann-Grad limit). The normalization factor is $\sqrt{t\log…
The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with…
A relation between the effective diffusion coefficient in a lattice with random site energies and random trasition rates and the macroscopic conductivity in a random resistor network allows for elucidating possible sources of anomalous…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We are discussing long-time, scaling limit for the anomalous diffusion composed of the subordinated L\'evy-Wiener process. The limiting anomalous diffusion is in general non-Markov, even in the regime, where ensemble averages of a…
We introduce a novel type of random perturbation for the classical Lorenz flow in order to better model phenomena slowly varying in time such as anthropogenic forcing in climatology and prove stochastic stability for the unperturbed flow.…
The Lorentz gas is one of the simplest, most widely used models to study the transport properties of rarified gases in matter. It describes the dynamics of a cloud of non-interacting point particles in an infinite array of fixed spherical…