论文标题
由粗糙信号驱动的Volterra方程3：volterra的概率构造粗糙的布朗动作的粗糙路径
Volterra equations driven by rough signals 3: Probabilistic construction of the Volterra rough path for fractional Brownian motions
论文作者
论文摘要
根据Volterra粗糙路径框架的最新发展，我们在这里考虑了与$ H> \ frac {1} {2} $相关的Volterra粗糙路径的概率结构，以及标准的Brownian Motion。对于某些$γ\ geq 0 $，允许Volterra内核$ k（t，s）$保持单数，并且表现类似于$ | t-s |^{ - γ} $。该结构都是在Stratonovich和ItôSense中完成的。它基于改良的Garsia-Rodemich-Romsey引理，该引理本身具有兴趣，以及Malliavin Colculus的工具。提供了有关挑战和潜在扩展的讨论。
Based on the recent development of the framework of Volterra rough paths, we consider here the probabilistic construction of the Volterra rough path associated to the fractional Brownian motion with $H>\frac{1}{2}$ and for the standard Brownian motion. The Volterra kernel $k(t,s)$ is allowed to be singular, and behaving similar to $|t-s|^{-γ}$ for some $γ\geq 0$. The construction is done in both the Stratonovich and Itô sense. It is based on a modified Garsia-Rodemich-Romsey lemma which has an interest in its own right, as well as tools from Malliavin calculus. A discussion of challenges and potential extensions is provided.
