Exponents, Symmetry Groups and Classification of Operator Fractional Brownian Motions

被引：0
作者：
Gustavo Didier
Vladas Pipiras
机构：
[1] Tulane University,Mathematics Department
[2] UNC-Chapel Hill,Dept. of Statistics and Operations Research
[3] Instituto Superior Técnico,CEMAT
来源：
Journal of Theoretical Probability | 2012年 / 25卷
关键词：
Operator fractional Brownian motions; Spectral domain representations; Operator self-similarity; Exponents; Symmetry groups; Orthogonal matrices; Commutativity; 60G18; 60G15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：353 / 395
页数：42
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