SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3681-3715, January 2021.
We prove a Wong--Zakai theorem for the defocusing stochastic mass-critical nonlinear Schrödinger equation on $\mathbb{R}$. The main ingredients are careful mixtures of bootstrapping arguments at both deterministic and stochastic levels. Several subtleties arising from the proof mark the difference between the dispersive case and corresponding situations in SDEs and parabolic stochastic PDEs, as well as the difference between the large-$n$ case and the limiting ($n=\infty$) case.

中文翻译：

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随机质量临界非线性薛定谔方程的Wong--Zakai定理

SIAM 数学分析杂志，第 53 卷，第 3 期，第 3681-3715 页，2021 年 1 月。
我们证明了 $\mathbb{R}$ 上散焦随机质量临界非线性薛定谔方程的 Wong--Zakai 定理。主要成分是在确定性和随机水平上仔细混合自举参数。证明产生的几个微妙之处标志着 SDE 和抛物线随机 PDE 中色散情况和相应情况之间的差异，以及大 $n$ 情况和限制 ($n=\infty$) 情况之间的区别。