论文标题
随机PDE通过凸流最小化
Stochastic PDEs via convex minimization
论文作者
论文摘要
我们证明了加权能量 - 散引血（WED）的适用性[50]以抽象形式以非线性抛物线抛物线随机偏微分方程为单位。 WED原理在于最小化参数依赖性凸的功能在整个轨迹上的功能。其独特的最小化器对应于随机差异问题的椭圆时期正常化。由于正则化参数趋于零，因此恢复了限制问题的解决方案。特别是，这通过凸优化提供了直接的批准，以实现非线性随机偏微分方程的近似值。
We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle [50] 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 approch via convex optimization to the approximation of nonlinear stochastic partial differential equations.
