  We consider collections of SDEs indexed by a graph. Each SDE is driven by an
additive Gaussian noise and each drift term interacts with all other SDEs
within the graph neighbourhood. We derive the fundamental martingale for a
class of Gaussian processes and use this to prove a Girsanov type theorem.
Further, we use this to construct a clique factorisation to prove that the law
of the interacting SDEs forms a 2-Markov Random Field.
