We calculated the noise correlation in a Gaussian stochastic process that is non-δ-function-correlated in both space and time. The colored noise obeys a linear reaction-diffusion Langevin equation with Gaussian white noise. Our result is a generalization of the Ornstein-Uhlenbeck process to take into account finite correlation in space as well as in time for colored noise.

• Received 12 July 1993

DOI:https://doi.org/10.1103/PhysRevE.48.3267