Elliptic gaussian random processes
Elliptic gaussian random processes
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DOI：
10.4171/rmi/217
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发表时间：
1997-04
影响因子：
1.2
通讯作者：
A. Benassi;Daniel Roux;S. Jaffard
中科院分区：
文献类型：
--
作者：
A. Benassi;Daniel Roux;S. Jaffard
本文研究了以Rd为指标的高斯随机场，其协方差一般定义为椭圆型伪微分算子的参数，并在符号上作了最小正则性假设。我们构造新的小波基适应这些运营商，在这个相应的基础上，该领域的分解产生其重对数律和一致的连续模。我们还刻画了局部标度的领域的伪微分算子的主符号的性质。对多重分数布朗运动也得到了类似的结果。
We study the Gaussian random fields indexed by Rd whose covariance is defined in all generality as the parametrix of an elliptic pseudo-differential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field in this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the fields in terms of the properties of the principal symbol of the pseudodifferential operator. Similar results are obtained for the Multi-Fractional Brownian Motion.