The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields
The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields
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DOI：
10.1016/j.spa.2017.05.003
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发表时间：
2015-11
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影响因子：
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通讯作者：
Ercan Sonmez
中科院分区：
文献类型：
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作者：
Ercan Sonmez
摘要设{X (t): t∈R d}是一个值在R m中的多元算子自相似随机场。在[22]中引入了这样的随机场，并且对所有c[22]满足标度性质{X (c E t): t∈R d}= d {c d X (t): t∈R d}，其中E是一个d× d实矩阵，d是一个m× m实矩阵。我们通过计算高斯情况下单位立方体K=[0,1] d上轨迹的范围和图的Hausdorff维数来解决[22]中的一个开放问题。特别地，我们启发了豪斯多夫维数由E和D的特征值的实部以及E和D的特征值的多重性决定的性质。
Abstract Let {X (t): t∈ R d} be a multivariate operator-self-similar random field with values in R m. Such fields were introduced in [22] and satisfy the scaling property {X (c E t): t∈ R d}= d {c D X (t): t∈ R d} for all c> 0, where E is a d× d real matrix and D is an m× m real matrix. We solve an open problem in [22] by calculating the Hausdorff dimension of the range and graph of a trajectory over the unit cube K=[0, 1] d in the Gaussian case. In particular, we enlighten the property that the Hausdorff dimension is determined by the real parts of the eigenvalues of E and D as well as the multiplicity of the eigenvalues of E and D.