Pathwise numerics and dynamics of stochastic evolution equations

每个有限维的Ito随机微分方程都可以转化为路径随机常微分方程，这意味着许多动力学性质可以路径地研究，数值计算不仅可以进行路径比较，而且还可以进行路径比较。这个联合方案的目的是研究这种路径等价是否也适用于随机发展方程，特别是半线性抛物型随机偏微分方程组，并在动力学和数值的背景下利用它。

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.