We show regularization effect of nonlinear gradient noise to the solution of 1D stochastic parabolic equation. We demonstrate convergence to a martingale (independent upon space variable) when we rescale noise at the extremum points of the process.

中文翻译：

---

重新调整一维随机抛物线方程的非线性噪声

我们展示了非线性梯度噪声对一维随机抛物方程解的正则化效果。当我们在过程的极值点重新调整噪声时，我们证明了收敛到鞅（独立于空间变量）。