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We consider a system of interacting diffusions on the integer lattice. Byletting the mesh size go to zero and by using a suitable scaling, we show thatthe system converges (in a strong sense) to a solution of the stochastic heatequation on the real line. As a consequence, we obtain comparison inequalitiesfor product moments of the stochastic heat equation with differentnonlinearities.

Strong invariance and noise-comparison principles for some parabolic stochastic PDEs