Different kinds of Parisi-Wu equations(parabolic or Schroedinger stochastic quantisation equations); Wave and dispersive PDEs; PKS equations; Cattaneo

我的第一个目标是建立具有几乎白噪声扰动的随机量子化方程的局部或整体存在性；给出一个物理解释；也许从第一原理推导出Parisi-Wu方程，这可能为我们解释量子力学的基本原理提供深远的见解。我的第二个目标是寻找连接随机分析和它们的非对易性质的桥梁，也许是通过著名的卡特内奥和费尔德公式。我的第三个目标是在更弱的条件下证明PKS系统的全球存在性，这将在后面详细说明。第一个目标将是主要目标。

My first goal is to establish the local or global existence of the stochastic quantisation equation with almost white noise disturbance; to give a physics interpretation; and perhaps to deduce Parisi-Wu equation from the first principle, which might provide far-reaching insights for one to interpret the fundamental principles of quantum mechanics. My second goal is to seek the bridge linking stochastic analysis and their noncommutative nature perhaps via the famous Cattaneo & Felder's formula. My third goal is to prove the global existence of PKS system under a more weaker condition, which will be explained in detail later. The first goal will be the major goal.