Some small ball probabilities for Gaussian processes under nonuniform norms
Some small ball probabilities for Gaussian processes under nonuniform norms
复制标题
非均匀范数下高斯过程的一些小球概率
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
Wolfgang Stolz
中科院分区：
文献类型：
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作者：
Wolfgang Stolz
本文建立了中心高斯过程（X（t））t∈[0，1]N在Hölder型范数下的小球概率的上下界以及一些更一般的泛函的上界.这推广了最近建立的一致范数的结果。此外，我们的下界证明相当简单。在特殊情况下N =1，我们建立精确的估计下更广泛的一类规范，特别是包括Besov规范。
We establish lower and upper bounds for the small ball probability of a centered Gaussian process(X(t))t∈[0,1]N under Hölder-type norms as well as upper bounds for some more general functionals. This extends recently established results for the uniform norm. In addition, our proof of the lower bound is considerably simpler. In the special caseN=1 we establish precise estimates under a wider class of norms including in particular the Besov norms.