论文标题
Hölder在抽象空间中不可或缺的Wiener积分的规律性
Hölder regularity of a Wiener integral in abstract space
论文作者
论文摘要
在本文中，我们提出了一种考虑一般集合$ \ MATHCAL {T} $的子集的集合$ \ Mathcal {a} $索引的过程。大量的矢量空间，歧管和连续$ \ mathbb {r} $ - 树是特定情况。晶格理论和拓扑假设被分别考虑，以阐明博览会。然后，我们为确定性函数$ f：\ natcal {a} $ in \ mathcal {a} $定义了wiener-type的积分$ y_a = \ int_a f \，\ text dx $，用于确定性函数$ f：\ mathcal {t} \ rightArrow \ rightArrow \ rightArrow \ Mathbb {r} $ and set-set-indexexexexexexexexexexexexexexexexexeced luty luty lutylévylutylévyvy$ x $ x $ x。这是Raput and Rosinski [40]的一个特殊情况，但是我们的设置可以更快地结构，并产生有关$ Y的样本路径的更多属性。$最后，给出了$ y $的hölder规律性的界限，这表明$ f $ and $ x $的规律性如何为$ y $贡献$ y $。这是贾法德[24]和Balança和Herbin [6]的作品。
In this article, we propose a way to consider processes indexed by a collection $\mathcal{A}$ of subsets of a general set $\mathcal{T}$. A large class of vector spaces, manifolds and continuous $\mathbb{R}$-trees are particular cases. Lattice-theoretic and topological assumptions are considered separately with a view to clarifying the exposition. We then define a Wiener-type integral $Y_A = \int_A f\,\text dX$ for all $A\in\mathcal{A}$ for a deterministic function $f:\mathcal{T} \rightarrow \mathbb{R}$ and a set-indexed Lévy process $X$. It is a particular case of Raput and Rosinski [40], but our setting enables a quicker construction and yields more properties about the sample paths of $Y.$ Finally, bounds for the Hölder regularity of $Y$ are given which indicate how the regularities of $f$ and $X$ contributes to that of $Y$. This follows the works of Jaffard [24] and Balança and Herbin [6].
