Small ball probabilities for smooth Gaussian fields and tensor products of compact operators
Small ball probabilities for smooth Gaussian fields and tensor products of compact operators
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光滑高斯场的小球概率和紧算子的张量积
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
A. Nazarov
中科院分区：
文献类型：
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作者：
A. I. Karol’;A. Nazarov
我们发现一类具有“张量积”结构的协方差的零均值高斯场的对数 L2-小球渐近。施加于边际协方差的主要条件是其特征值的计数函数的起源处的缓慢增长。这对于具有平滑协方差的高斯函数是有效的。在积分的特殊自相似测度的情况下，还考虑的另一种类型的边际函数是经典维纳过程、布朗桥、奥恩斯坦-乌伦贝克过程等。我们的结果基于希尔伯特空间中紧自伴随算子张量积的谱渐近新定理，该定理具有独立意义。因此，我们继续开发论文中提出的方法，其中假设边际特征值无穷大时的常规行为。
We find the logarithmic L2‐small ball asymptotics for a class of zero mean Gaussian fields with covariances having the structure of “tensor product”. The main condition imposed on marginal covariances is slow growth at the origin of counting functions of their eigenvalues. That is valid for Gaussian functions with smooth covariances. Another type of marginal functions considered as well are classical Wiener process, Brownian bridge, Ornstein–Uhlenbeck process, etc., in the case of special self‐similar measure of integration. Our results are based on a new theorem on spectral asymptotics for the tensor products of compact self‐adjoint operators in Hilbert space which is of independent interest. Thus, we continue to develop the approach proposed in the paper , where the regular behavior at infinity of marginal eigenvalues was assumed.
影响因子：
0.8
作者：
F. Aurzada;F. Gao;T. Kühn;W. V. Li;Q.-M. Shao
通讯作者：
Q.-M. Shao