Regularity of Gaussian Processes on Dirichlet Spaces
Regularity of Gaussian Processes on Dirichlet Spaces
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DOI：
10.1007/s00365-018-9416-8
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发表时间：
2015-08
影响因子：
2.7
通讯作者：
G. Kerkyacharian;Shigeyoshi Ogawa;P. Petrushev;D. Picard
中科院分区：
文献类型：
--
作者：
G. Kerkyacharian;Shigeyoshi Ogawa;P. Petrushev;D. Picard
研究了紧度量空间中的中心高斯过程的正则性。证明了在（i）M上存在决定Besov正则性的基础Dirichlet结构，且（ii）具有核K（x，y）的算子K与Dirichlet结构的基础算子A可交换的假设下，这类过程的几乎处处Besov正则性（几乎）等价于协方差的Besov正则性.作为这一结果的应用，我们建立了紧齐性空间，特别是，由球指标的高斯过程的Besov正则性。
We study the regularity of centered Gaussian processes, indexed by compact metric spaces. It is shown that the almost everywhere Besov regularity of such a process is (almost) equivalent to the Besov regularity of the covarianceunder the assumption that (i) there is an underlying Dirichlet structure onMthat determines the Besov regularity, and (ii) the operatorKwith kernelK(x,y) and the underlying operatorAof the Dirichlet structure commute. As an application of this result, we establish the Besov regularity of Gaussian processes indexed by compact homogeneous spaces and, in particular, by the sphere.