  We introduce a general formalism to describe the effects of Markovian noise
which is spatially correlated, typically decaying over some finite correlation
length. For any system of interest, this formalism describes spatial
correlations without the necessity to choose a particular microscopic model for
the environment. We present a method of mapping the equations to Lindblad form
and discuss functional forms for homogeneous spatial correlation functions. We
also discuss two example microscopic models for the environment which exhibit
non-trivial spatial-temporal correlation functions.
