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Stochastic quantization is a novel way of computing the Green functions of a physical theory as the long time limits of the correlators of a suitably constructed Langevin equation. It is well known that the correlators of the Langevin equation can be calculated as Green functions of a topological field theory. We show that the action of the topological field theory which computes the correlators of the Langevin equation is a closed equivariant form on an infinite dimensional symplectic manifold with a Hamiltonian group action. The random source which drives the Langevin equation is interpreted as a moment map associated with the Hamiltonian group action. We also identify,up to grading, the BRST complex of the topological theory as a Cartan model of equivariant cohomology.