论文标题
噪音无噪声正规化
Noiseless regularisation by noise
论文作者
论文摘要
我们分析了通用连续添加扰动对普通微分方程良好性的影响。从流行的意义上讲，这里的通用性是可以理解的。这使我们能够在不必对扰动的统计属性的任何限制性假设中讨论这些问题。主要结果是，通用连续扰动为任意不规则的矢量场提供了库奇问题。因此，我们通过噪声“没有概率”来建立正则化。
We analyse the effect of a generic continuous additive perturbation to the well-posedness of ordinary differential equations. Genericity here is understood in the sense of prevalence. This allows us to discuss these problems in a setting where we do not have to commit ourselves to any restrictive assumption on the statistical properties of the perturbation. The main result is that a generic continuous perturbation renders the Cauchy problem well-posed for arbitrarily irregular vector fields. Therefore we establish regularisation by noise "without probability".
