We study noise-induced transitions when the system is driven separately by a Gaussian colored noise and a non-Gaussian bounded noise with the same mean and stationary correlation. Clear differences in the nature of such transitions for these two cases are observed. These transitions are shown to...

We give a strict comparison of the diffusion, Bourret, and van Kampen approximations in the analysis of stochastic equations with short correlation time disturbances through the example of a random harmonic oscillator. We show that the diffusion approximation does not always gives satisfactory...

The paper discusses some problems in applications of closure techniques to moment hierarchies by considering the equation of the overdamped oscillator with cubic nonlinearity and additive Gaussian white noise. It is rigorously shown that some closure schemes can be inconsistent in spite of they...