  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 is given. The process is
an alternative to a recently proposed spatiotemporal correlated model process
[J. Garcia-Ojalvo et al., Phys. Rev. A 46, 4670 (1992)] for which we calculate
explicitely the hitherto not known autocorrelation function in real space.
