随机偏微分方程（英文：Stochastic partial differential equations (SPDEs)）类似于一般的随机微分方程。其本质上是带有随机项和随机系数的偏微分方程。随机微分方程在量子场论、统计力学、金融数学中有着广泛的应用。
Examples.One of the most studied SPDEs is the stochastic heat equation, which may formally be written aswhere form