Conformal invariance of white noise
Conformal invariance of white noise
复制标题
白噪声的共形不变性
DOI：
10.1017/s0027763000021383
复制
发表时间：
1985
影响因子：
0.8
通讯作者：
Sheu
中科院分区：
文献类型：
--
作者：
T. Hida;Ke;Sheu
白色噪声的结构和无限维旋转群的结构之间的显著联系已经被概率论和谐波分析中的各种方法所证明。当白色噪声的时间参数空间的维数增加时，这种联系自然变得更加复杂。说明这种情况的有力方法之一是观察无限维旋转群的某些子群的结构，这些子群来自时间参数空间的超同态，即时间变化。事实上，这些分组将揭示隐藏在通常的正式观察背后的概率意义。此外，子群通常描述了由白色噪声形成的高斯随机场的时间参数在基本参数空间上运行时的依赖方式。本文的主要目的是引入无限维旋转群的有限维子群，它们具有重要的概率意义，并讨论它们在概率论中的作用。特别是，我们将看到，共形不变性的白色噪音可以描述的共形群，这是一个有限维李群的无限维旋转。
The remarkable link between the structure of the white noise and that of the infinite dimensional rotation group has been exemplified by various approaches in probability theory and harmonic analysis. Such a link naturally becomes more intricate as the dimension of the time-parameter space of the white noise increases. One of the powerful method to illustrate this situation is to observe the structure of certain subgroups of the infinite dimensional rotation group that come from the diffeomorphisms of the time-parameter space, that is the time change. Indeed, those subgroups would shed light on the probabilistic meanings hidden behind the usual formal observations. Moreover, the subgroups often describe the way of dependency for Gaussian random fields formed from the white noise as the time-parameter runs over the basic parameter space. The main purpose of this note is to introduce finite dimensional subgroups of the infinite dimensional rotation group that have important probabilistic meanings and to discuss their roles in probability theory. In particular, we shall see that the conformal invariance of white noise can be described in terms of the conformal group which is a finite dimensional Lie subgroup of the infinite dimensional rotation group.