论文标题
在A.S.定理上Cherny用于半线性随机部分微分方程
On a Theorem by A.S. Cherny for Semilinear Stochastic Partial Differential Equations
论文作者
论文摘要
我们考虑对半线性随机部分微分方程的分析解决方案，其由圆柱布朗尼运动驱动的非预期系数。允许解决方案在一般可分开的Banach空间中取值。我们表明，弱唯一性等同于弱关节唯一性，从而概括了A.S.定理的定理。 Cherny到无限的尺寸设置。我们对技术关键步骤的证明不同于Cherny's，并使用圆柱形的Martingale问题。作为应用程序，我们推断出Yamada-Watanabe定理的双重版本，即，我们表明存在强大的存在和弱独特意味着存在薄弱和独特性。
We consider analytically weak solutions to semilinear stochastic partial differential equations with non-anticipating coefficients driven by cylindrical Brownian motion. The solutions are allowed to take values in general separable Banach spaces. We show that weak uniqueness is equivalent to weak joint uniqueness, and thereby generalize a theorem by A.S. Cherny to an infinite dimensional setting. Our proof for the technical key step is different from Cherny's and uses cylindrical martingale problems. As an application, we deduce a dual version of the Yamada-Watanabe theorem, i.e. we show that strong existence and weak uniqueness imply weak existence and strong uniqueness.
