This work is concerned with non-equilibrium phenomena, with focus on the numerical simulation of the relaxation of non-conserved order parameters described by stochastic kinetic equations known as GinzburgLandau-Langevin (GLL) equations. We propose methods for solving numerically these type of equations, with additive and multiplicative noises. Illustrative applications of the methods are prese...

The individual motion of a colloidal particle is described by an overdamped Langevin equation. When rotational degrees of freedom are relevant, these are described by a corresponding Langevin process. Our purpose is to show that the microscopic local density of colloids, in terms of a space and rotation state, also evolves according to a Langevin equation. The latter can then be used as the sta...

We consider a multivariate Langevin equation in discrete time, driven by a force induced by certain Gibbs' states. The main goal of the paper is to study the asymptotic behavior of a random walk with stationary increments (which are interpreted as discrete-time speed terms) satisfying the Langevin equation. We observe that (stable) functional limit theorems and laws of iterated logarithm for re...

The role of external forces in systems exhibiting anomalous diffusion is discussed on the basis of the describing Langevin equations. Since there exist different possibilities to include the effect of an external field the concept of biasing and decoupled external fields is introduced. Complementary to the recently established Langevin equations for anomalous diffusion in a time-dependent exter...

In this note we study the asymptotic limit of large variance in a stochastically perturbed thermostat model, the Nosé-Hoover-Langevin device. We show that in this limit, the model reduces to a Langevin equation with one-dimensional Wiener process, and that the perturbation is in the direction of the conjugate momentum vector. Numerical experiments with a double well potential corroborate the as...