论文标题
非线性年轻微分方程：评论
Nonlinear Young differential equations: a review
论文作者
论文摘要
非线性年轻积分首先是在[Catellier，Gubinelli，Spa 2016]中引入的，并提供了经典的年轻人的自然概括，但也提供了通过噪声现象对正则化的途径研究中的多功能工具。我们在这里介绍了对该理论的独立描述，重点是抽象非线性年轻微分方程的良好性结果，以及一些新的扩展。还治疗了数值方案和非线性年轻PDE的收敛性。除非明确说明，否则大多数结果都是针对一般（可能是无限维度）的Banach空间的（可能是无限的）Banach空间，并且不使用紧凑性假设。
Nonlinear Young integrals have been first introduced in [Catellier,Gubinelli, SPA 2016] and provide a natural generalisation of classical Young ones, but also a versatile tool in the pathwise study of regularisation by noise phenomena. We present here a self-contained account of the theory, focusing on wellposedness results for abstract nonlinear Young differential equations, together with some new extensions; convergence of numerical schemes and nonlinear Young PDEs are also treated. Most results are presented for general (possibly infinite dimensional) Banach spaces and without using compactness assumptions, unless explicitly stated.
