Weak convergence of interacting SDEs to the superprocess

A finite system of stochastic differential equations defined on a lattice w ith nearest-neighbor interaction is scaled so that the distance between lat tice sites decreases and the size of the system increases. The space-time p rocess defined by the above system is shown to converge in law to the solut ion of the SPDE associated with the super-Brownian motion on [0, 1].