A solution of the Ornstein-Uhlenbeck equation (Q816021)

The authors provide a solution to the Ornstein-Uhlenbeck equation based on a random walk with the random movement taken by sampled points of a random signal. The random signal is a sum of sine functions with random amplitudes, random frequencies, and random phases. At variance with solutions by other methods, they show that the Lyapunov exponent of their solution is positive by proving that the power of the signal has the additive property.