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A one dimensional stochastic differential equation of the form dX = The equation is equipped with periodic boundary conditions. When α = 0 this equation arises in the Kardar-Parisi-Zhang model. For α = 0, this equation conserves two important properties of the Kardar-Parisi-Zhang model: it contains a quadratic nonlinear term and has an explicit invariant measure which is gaussian. However, it is not as singular and using renormalization and a fixed point result we prove existence and uniquenessdoi:10.1214/ecp.v12-1333 fatcat:oorw3yk7jnbkbdq6eadizdgyku