  We develop and implement new probabilistic strategy for proving basic results
about long time behaviour for interacting diffusion processes on unbounded
lattice. The concept of the solution used is rather weak as we construct the
process as a solution to suitable infinite dimensional martingale problem.
However the techniques allow us to consider cases where the generator of the
particle is degenerate elliptic operator. As a model example we present
situation, where the operator arises from Heisenberg group. In the last section
we mention some further examples that can be handled using our methods.
