Pathwise numerics and dynamics of stochastic evolution equations

每一个有限维的Ito随机微分方程都可以转化为一个路径随机常微分方程，这意味着许多动力学性质可以在路径上研究，不仅可以进行数值计算，而且可以进行路径上的比较.这个联合提案的目的是调查，如果这样的路径等价也适用于随机发展方程，特别是半线性抛物随机偏微分方程，并利用它的动力学和数值的背景下。

Every finite dimensional Ito stochastic differential equation can be transformed into a pathwise random ordinary differential equation, which means that many dynamical properties can be investigated pathwise and numerical calculations can not only be carried out but also compared pathwise. The aim of this joint proposal is to investigate if such a pathwise equivalence also holds for stochastic evolution equations, in particular for semilinear parabolic stochastic partial differential equations and to exploit it in the context of dynamics and numerics.