A numerical simulation algorithm that is exact for any time step Δt> 0 is derived for the
Ornstein-Uhlenbeck process X (t) and its time integral Y (t). The algorithm allows one to …

Spectral and pseudospectral methods have become increasingly popular as higher order
methods for the solution of partial differential and integral equations (Azaïez et al. 2013). A …

Stochastic delay systems with additive noise are examined from the perspective of Fokker-
Planck equations. For a linear system, the exact stationary probability density is derived by …

We present a simple and systematic procedure to determine the effective dynamics of a
Brownian particle coupled to a rapidly fluctuating correlated medium, modeled as a scalar …

Multistable systems can exhibit stochastic resonance which is characterized by the
amplification of small periodic signals by additive noise. Here we consider a nonmultistable …

The dynamics and the steady states of a point-like tracer particle immersed in a confined
critical fluid are studied. The fluid is modeled field-theoretically in terms of an order …

Smoothed Wigner transforms have been used in signal processing, as a regularized version
of the Wigner transform, and have been proposed as an alternative to it in the …

Abstract The Fokker–Planck equation with a constant diffusion coefficient and a particular
polynomial drift coefficient can exhibit a bistable equilibrium distribution. Such model …

We consider one-dimensional anomalous diffusion of free Brownian particle. A time-
dependent probability density function for search process was obtained based on …

Non-Markovian effects on the Brownian movement of a free particle in the presence as well
as in the absence of inertial force are investigated under the framework of generalized …