Exponents, Symmetry Groups and Classification of Operator Fractional Brownian Motions

Gustavo Didier; Vladas Pipiras

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Exponents, Symmetry Groups and Classification of Operator Fractional Brownian Motions

机译：算符分数布朗运动的指数，对称群和分类

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Operator fractional Brownian motions (OFBMs) are zero mean, operator self-similar (o.s.s.) Gaussian processes with stationary increments. They generalize univariate fractional Brownian motions to the multivariate context. It is well-known that the so-called symmetry group of an o.s.s. process is conjugate to subgroups of the orthogonal group. Moreover, by a celebrated result of Hudson and Mason, the set of all exponents of an operator self-similar process can be related to the tangent space of its symmetry group.

机译：算子分数布朗运动（OFBMs）为零均值，算子自相似（o.s.s.）高斯过程，具有固定增量。他们将单变量分数布朗运动推广到多元上下文。众所周知，所谓的对称对称群。该过程与正交组的子组共轭。此外，通过哈德森（Hudson）和梅森（Mason）的著名结果，算子自相似过程的所有指数集可以与其对称组的切线空间有关。

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来源
《Journal of Theoretical Probability》 |2012年第2期|p.353-395|共43页
作者
Gustavo Didier; Vladas Pipiras;
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作者单位

Mathematics Department, Tulane University, 6823 St. Charles Avenue, New Orleans, LA, 70118, USA;

Dept. of Statistics and Operations Research, UNC-Chapel Hill, CB#3260, Smith Bldg., Chapel Hill, NC, 27599, USA;

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正文语种 eng
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关键词
Operator fractional Brownian motions; Spectral domain representations; Operator self-similarity; Exponents; Symmetry groups; Orthogonal matrices; Commutativity; 60G18; 60G15;

机译：算子分数布朗运动;谱域表示;算子自相似性;指数;对称群;正交矩阵;可交换性;60G18;60G15;

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Exponents, Symmetry Groups and Classification of Operator Fractional Brownian Motions

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