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We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…

We introduce a simple model of deterministic particles in weakly disordered media which exhibits a transition from normal to anomalous diffusion. The model consists of a set of non-interacting overdamped particles moving on a disordered…

We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…

Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Levy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process…

We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…

Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is…

This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…

An oxidation process is simulated for a bundle of metal tubes in a cross-flow. A fluid flow is governed by the incompressible Navier-Stokes equations. To describe the transport of oxygen, the corresponding convection-diffusion equation is…

We consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate (the tube axis). Inside the random tube, which is stationary and ergodic, non-interacting particles move…

We present two limit theorems, a mean ergodic and a central limit theorem, for a specific class of one-dimensional diffusion processes that depend on a small-scale parameter $\varepsilon$ and converge weakly to a homogenized diffusion…

Light diffusion is usually associated with thick, opaque media. Indeed, multiple scattering is necessary for the onset of the diffusive regime and such condition is generally not met in almost transparent media. Nonetheless, at long enough…

Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…

The paper addresses the single-file diffusion in the presence of an absorbing boundary. The emphasis is on an interplay between the hard-core interparticle interaction and the absorption process. The resulting dynamics exhibits several…

In parallel with advances in microscale imaging techniques, the fields of biology and materials science have focused on precisely extracting particle properties based on their diffusion behavior. Although the majority of real-world…

We simulate the granular flow in a narrow pipe with a lattice-gas automaton model. We find that the density in the system is characterized by two features. One is that spontaneous density waves propagate through the system with well-defined…

There is no agreement in the literature on the rate of diffusion of a particle in a cooling granular gas. Predictions and model assumptions range from the conventional to very exotic dependence of the mean square distance (MSD) on time.…

We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

We consider subdiffusion of a particle in a one-dimensional system with a thin partially permeable wall. Passing through the wall, the particle can be absorbed with a certain probability. We call such a wall partially permeable partially…