论文标题
$ρ$ irregularity和相关属性的患病率
Prevalence of $ρ$-irregularity and related properties
论文作者
论文摘要
We show that generic Hölder continuous functions are $ρ$-irregular. Catellier和Gubinelli（stoc。proc。Appl。126，2016）首先引入了$ρ$ - 偶然性的财产，并在某些类似扰动的ODES和PDE的研究中起着关键作用。 Genericity here is understood in the sense of prevalence.结果，我们通过噪声“无概率”获得了几个关于正则化的结果，即不承诺对扰动的统计特性的特定假设。我们还为随机过程建立了有用的标准，为$ρ$ irrentarbul，并详细研究$ρ$ irrongular函数的几何和分析特性。
We show that generic Hölder continuous functions are $ρ$-irregular. The property of $ρ$-irregularity has been first introduced by Catellier and Gubinelli (Stoc. Proc. Appl. 126, 2016) and plays a key role in the study of well-posedness for some classes of perturbed ODEs and PDEs. Genericity here is understood in the sense of prevalence. As a consequence we obtain several results on regularisation by noise "without probability", i.e. without committing to specific assumptions on the statistical properties of the perturbations. We also establish useful criteria for stochastic processes to be $ρ$-irregular and study in detail the geometric and analytic properties of $ρ$-irregular functions.
