Copyright © 2010 John F. Moxnes and Kjell Hausken. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We incorporate randomness into deterministic theories and compare analytically and numerically some well-known stochastic theories: the Liouville process, the Ornstein-Uhlenbeck process, and a process that is Gaussian and exponentially time correlated (Ornstein-Uhlenbeck noise). Different methods of achieving the marginal densities for correlated and uncorrelated noise are discussed. Analytical results are presented for a deterministic linear friction force and a stochastic force that is uncorrelated or exponentially correlated.