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A rigorous equation is stated and it is shown that the spatial derivative ofthe Cole-Hopf solution of the KPZ equation is a solution of this equation. Themethod of proof used to show that a process solves this equation is based onrather weak estimates so that this method has the advantage that it could beused to verify solutions of other highly singular SPDEs, too.

A rigorous equation for the Cole-Hopf solution of the conservative KPZ equation