论文标题
无限尺寸空间上的几何粗糙路径
Geometric rough paths on infinite dimensional spaces
论文作者
论文摘要
与普通的微分方程相似，可以在Banach空间设置中配制粗糙的路径和粗糙的差分方程。对于$α\在（1/3,1/2）$中，我们给出标准的标准，何时可以通过有界变化的曲线签名（鉴于Hölder参数的某些调音）来近似Banach空间价值弱的几何$α$ -1ROUGH路径。我们表明，对于希尔伯特空间上弱的几何粗糙路径，这些标准满足了这些标准。作为一种应用，我们使用（无界）粗糙驱动程序的概念获得了功能空间值的Wong-Zakai类型。
Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For $α\in (1/3,1/2)$, we give criteria for when we can approximate Banach space-valued weakly geometric $α$-rough paths by signatures of curves of bounded variation, given some tuning of the Hölder parameter. We show that these criteria are satisfied for weakly geometric rough paths on Hilbert spaces. As an application, we obtain Wong-Zakai type result for function space valued martingales using the notion of (unbounded) rough drivers.
