Operator scaling stable random fields
Operator scaling stable random fields
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DOI：
10.1016/j.spa.2006.07.004
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发表时间：
2007-03-01
影响因子：
1.4
通讯作者：
Scheffler, Hans-Peter
中科院分区：
文献类型：
--
作者：
Bierme, Hermine;Meerschaert, Mark M.;Scheffler, Hans-Peter
一个标量值随机场(X(X)}(x是RD的一个元素)称为算子标度，如果对某个d×d矩阵E有正实部的特征值和一些H>；0，我们有{X(c(E)x)}(x是RD的元素)=F.D.对所有c>；0，{c(H)X(X)}(x是RD的一个元素)，其中=(F.D)。表示所有有限维边缘分布相等。利用所谓的E齐次函数Phi，满足Phi(c(E)x)=c Phi(X)，给出了稳定算子标度随机场的滑动平均和调和表示.这些场也具有稳定的增量，并且是随机连续的。在高斯情形下，还得到了样本轨道的临界Holder指数和Hausdorff维。(C)2006爱思唯尔B.V.保留所有权利。
A scalar valued random field (X(x)}(x is an element of Rd) is called operator-scaling if for some d x d matrix E with positive real parts of the eigenvalues and some H > 0 we have{X(c(E)x)}(x is an element of Rd) =f.d. {c(H) X (x)}(x is an element of Rd) for all c > 0,where =(f.d). denotes equality of all finite-dimensional marginal distributions. We present a moving average and a harmonizable representation of stable operator scaling random fields by utilizing so called E-homogeneous functions phi, satisfying phi(c(E)x) = c phi(x). These fields also have stationary increments and are stochastically continuous. In the Gaussian case, critical Holder-exponents and the Hausdorff-dimension of the sample paths are also obtained. (C) 2006 Elsevier B.V. All rights reserved.