Abstract We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle to nonlinear parabolic stochastic partial differential equations in abstract form. The WED principle consists in the minimization of a parameter-dependent convex functional on entire trajectories. Its unique minimizers correspond to elliptic-in-time regularizations of the stochastic differential problem. As the regularization parameter tends to zero, solutions of the limiting problem are recovered. This in particular provides a direct approach via convex optimization to the approximation of nonlinear stochastic partial differential equations.

中文翻译：

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通过凸最小化的随机偏微分方程

摘要 我们以抽象形式证明了加权能量耗散 (WED) 变分原理对非线性抛物线随机偏微分方程的适用性。WED 原理包括在整个轨迹上最小化依赖于参数的凸函数。其独特的最小化器对应于随机微分问题的椭圆时间正则化。随着正则化参数趋于零，极限问题的解被恢复。这特别提供了一种通过凸优化来逼近非线性随机偏微分方程的直接方法。