论文标题
噪声扰动的ODE的c-内正则化
C-infinity regularization of ODEs perturbed by noise
论文作者
论文摘要
我们研究了一般Schwartz分布给出的矢量场的ODES，我们表明，如果我们通过添加“无限正规化”路径来扰动这种方程，那么它具有独特的解决方案并诱导了无限平稳的差异性流动。我们还引入了一个标准，在该标准下，高斯过程的样本路径是无限正规化的，我们提出了满足我们标准的两个过程。结果基于当地时代的路径时空规则性特性，并使用基于非线性年轻积分的Catellier-Gubinelli的方法构建溶液。
We study ODEs with vector fields given by general Schwartz distributions, and we show that if we perturb such an equation by adding an "infinitely regularizing" path, then it has a unique solution and it induces an infinitely smooth flow of diffeomorphisms. We also introduce a criterion under which the sample paths of a Gaussian process are infinitely regularizing, and we present two processes which satisfy our criterion. The results are based on the path-wise space-time regularity properties of local times, and solutions are constructed using the approach of Catellier-Gubinelli based on non-linear Young integrals.
