Exponents of operator self-similar random fields

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• 作者：Gustavo Didier^a ; ^{gdidier@tulane.edu} ; Mark M. Meerschaert^b ; ^{mcubed@stt.msu.edu} ; Vladas Pipiras^c ; ^{pipiras@email.unc.edu}
• 关键词：Operator self-similar random fields ; Gaussian random fields ; Operator scaling ; Operator self-similarity ; Anisotropy
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：1450-1466
• 全文大小：469 K
• 卷排序：448

文摘

If X(cEt)X(cEt) and cHX(t)cHX(t) have the same finite-dimensional distributions for some pair of linear operators E and H  , we say that the random vector field X(t)X(t) is operator self-similar. The exponents E and H are not unique in general, due to symmetry. This paper characterizes the possible set of range exponents H for a given domain exponent, and conversely, the set of domain exponents E for a given range exponent.