We prove a version of the Wong-Zakai theorem for one-dimensional parabolic nonlinear stochastic PDEs driven by space-time white noise. As a corollary, we obtain a detailed local description of solutions.
Martin HAIRER. Étienne PARDOUX. "A Wong-Zakai theorem for stochastic PDEs." J. Math. Soc. Japan 67 (4) 1551 - 1604, October, 2015. https://doi.org/10.2969/jmsj/06741551