new definition of solutions to heat-based spde

We start by introducing a new definition of solutions to heat-basedspdes driven by space-time white noise: sddes(stochastic differential-difference equations) limits solutions.we also examine briefly,through order parameters $epsilon_1$ and $epsilon_2$ multiplied by thelaplacian and the noise, the effect of letting$epsilon_1,epsilon_2to 0$ at different speeds. more precisely,it is shown that the ratio $epsilon_2/epsilon_1^{1/4}$ determinesthe behavior as $epsilon_1,epsilon_2to 0$.similar to the zero drift case the equivalence assertion in lemma ref{gsdde} follows as in the continuous time-space case from an equivalence of test function and green functionformulations argument, and the existence is a straightforward generalization of standard sdes arguments and the details will be omitted.