Generation of spatiotemporal correlated noise in $1+1$ dimensions

We propose a generalization of the Ornstein-Uhlenbeck process in $1+1$ dimensions which is the product of a temporal Ornstein-Uhlenbeck process with a spatial one and has exponentially decaying autocorrelation. The generalized Langevin equation of the process, the corresponding Fokker-Planck equation, and a discrete integral algorithm for numerical simulation are given. The process is an alternative to a recently proposed spatiotemporal correlated model process [J. García-Ojalvo et al., Phys. Rev. A 46, 4670 (1992)] for which we calculate explicitly the hitherto unknown autocorrelation function in real space.