Stochastic Analysis on nonlinear sets

本文给出了高斯空间中凸集的一个发散公式，它包括了一般的维纳空间。我们发现，在高斯测度下的过程的极大值的某种规律性起着至关重要的作用，而不是马尔可夫性质，这是相信。我们还成功地恢复已知的公式，然后使用马尔可夫性质，这是我们的分歧公式的具体表达。我们还得到了分形集上渗流的临界概率。我们已经成功地可视化相互作用的粒子的运动，解决方案的随机偏微分方程驱动的Levy型噪声。

We have formulated a divergence formula on convex sets in the Gaussian space which include usual Wiener spaces. We found that a certain regularity of the maximal of the processes under the Gaussian measure plays an essential role rather than Markov properties which was believed. We also succeeded in recovering known formulae using Markov properties then, which is a concrete expression of our divergence formulae. We have also obtained a critical probability for a percolation on a fractal set. We have succeeded in visualizing a motion of interacting particles, solutions to stochastic partial differential equations driven by Levy type noises.