In this article we take into account a class of stochastic space diffusion equations with polynomials forced by additive noise. We derive rigorously limiting equations which de…ne the critical dynamics. Also, we approximate solutions of stochastic fractional space di¤usion equations with polynomial term by limiting equations, which are ordinary di¤er-ential equations. Moreover, we address the e¤ect of the noise on the solution’s stabilization. Finally, we apply our results to Fisher’s equation and Ginzburg–Landau models.
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