高斯周期过程的一个标准型
A canonical form for Gaussian periodic processes
摘要：
本文给出了一组高斯过程的一个表示定理，该定理允许构造具有任意正则性的高斯过程，并将其表示为随机三角级数的极限.我们通过Karhunen-Love定理证明了这个集合等距等价于l2。然后，我们证明，任何这样的过程的轨迹路径的规律性，可以检测到只是通过寻找与他通过等距l2序列的减少率。
英文摘要：
This article provides a representation theorem for a set of Gaussian processes; this theorem allows to build Gaussian processes with arbitrary regularity and to write them as limit of random trigonometric series. We show via Karhunen-Love theorem that this set is isometrically equivalent to l2. We then prove that regularity of trajectory path of anyone of such processes can be detected just by looking at decrease rate of l2 sequence associated to him via isometry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
