Stochastic runaway of dynamical systems (Q1116202)

It may happen that a Markovian process does not allow a stationary solution (e.g. the Wiener process). Usually, this is not easy to check. However, for a subclass of N-dimensional processes which can be described as stochastic dynamical systems, sufficient criteria can be given in a relatively simple form. As a byproduct, it turns out that entropy diverges in the sense of growing uncertainty. The resulting asymptotic, complete flattening of the distribution function is called stochastic runaway. Examples such as reflection of a plane wave from a half-space with random refraction index are treated and counter examples are given.