论文标题
奇异路径空间和应用
Singular paths spaces and applications
论文作者
论文摘要
最新在粗糙的波动性和规律性结构中的应用，尤其是奇异建模分布的概念，我们研究了零以零的奇异性的路径，粗糙路径和相关对象。在纯路径设置中，这使我们能够利用现有的SLE BESOV估计值，以确保SLE痕迹在单一的Hölder空间中需要值，该空间量化了该制度$κ<1 $中的众所周知的边界效应。然后，我们考虑针对奇异粗糙路径及其一些扩展的整合理论。从规律性结构的角度来看，这提供了一种调和的方法，用于构建（分数）粗糙的波动率模型的不同奇异内核，以及对固定案例的有效降低，这对于应用一般的重构化方法至关重要。
Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path setting this allows us to leverage on existing SLE Besov estimates to see that SLE traces takes values in a singular Hölder space, which quantifies a well-known boundary effect in the regime $κ< 1$. We then consider the integration theory against singular rough paths and some extensions thereof. This gives a method to reconcile, from a regularity structure point of view, different singular kernels used to construct (fractional) rough volatility models and an effective reduction to the stationary case which is crucial to apply general renormalisation methods.
