From Markovian to non-Markovian stochastic processes: Diffusion coefficients with power law time dependence.

The link between Markovian and non-Markovian stochastic processes is examined by looking at the drift and diffusion coefficients. Starting with the Langevin equation, a solution for the Fokker-Planck equation is obtained using white noise analysis. An evaluation of the mean square displacement explicitly shows that the drift coefficient may not play a crucial role in transitions from Markovian to non-Markovian processes. A special case of the solution obtained for the Fokker-Planck equation is fractional Brownian motion which we use to consider absorbing boundaries. [ABSTRACT FROM AUTHOR]