论文标题
维纳噪声上的固定局部随机可数集
Stationary local random countable sets over the Wiener noise
论文作者
论文摘要
布朗当地的最小值，马克西玛（Maxima）及其结合的时代是与经典维纳噪声相关的局部，固定，密集，随机可数集的三个截然不同的例子。作为局部平均值，大致是由布朗运动样本路径的局部行为确定的，而固定的固定均值表示相对于样品路径的lévy偏移而不变。我们回答了Tsirelson的肯定问题，是否还有其他问题，并为这种集合发展了一些一般理论。其结构的额外成分，即诚实的索引，导致分裂结果，类似于以最小（或最大值）的最小（或最大值）的维纳 - hopf分解，后者是特殊情况。此外，表明承认诚实索引的集合具有没有停止时间属于它们的财产。它们也很少：它们没有任何非空的当地固定子集。诚实地索引或以其他方式研究的那种随机集，引起了非经典的一维噪声，从而推广了分裂的噪音。研究了这些噪音的某些特性及其之间的相互关系。特别是，子集连接到亚措施。
The times of Brownian local minima, maxima and their union are three distinct examples of local, stationary, dense, random countable sets associated with classical Wiener noise. Being local means, roughly, determined by the local behavior of the sample paths of the Brownian motion, and stationary means invariant relative to the Lévy shifts of the sample paths. We answer to the affirmative Tsirelson's question, whether or not there are any others, and develop some general theory for such sets. An extra ingredient to their structure, that of an honest indexation, leads to a splitting result that is akin to the Wiener-Hopf factorization of the Brownian motion at the minimum (or maximum) and has the latter as a special case. Sets admitting an honest indexation are moreover shown to have the property that no stopping time belongs to them with positive probability. They are also minimal: they do not have any non-empty proper local stationary subsets. Random sets, of the kind studied in this paper, honestly indexed or otherwise, give rise to nonclassical one-dimensional noises, generalizing the noise of splitting. Some properties of these noises and the inter-relations between them are investigated. In particular, subsets are connected to subnoises.
