Using the Langevin equations, we calculated the stationary second-order moment (mean-square displacement) of a stochastic harmonic oscillator subject to an additive random force (Brownian motion in a parabolic potential) and to different types of multiplicative noise (random frequency or random...

In addition to the case usually considered of a stochastic harmonic oscillator subject to an external random force (Brownian motion in a parabolic potential) or to a random frequency and random damping, we consider an oscillator with random mass subject to an external periodic force, where the...

The phenomenon of ‘synchronization’ of physical diffusion is widely discussed in the physical literature. In this paper, we give a simple rigorous proof of the synchronization for a one-dimensional diffusion including the one-dimensional counterpart of a physical diffusion described by a...