Singularity among selfsimilar Gaussian random fields with different scaling parameters and others
Ma, Chunsheng
Ma, Chunsheng
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2018-11-02
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Article
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Keywords
Singularity for measures,Selfsimilar,Schoenberg-Levy kernel,Positive definite,Stationary
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Chunsheng Ma (2018) Singularity among selfsimilar Gaussian random fields with different scaling parameters and others, Stochastic Analysis and Applications, 36:6, 996-1005
Abstract
It is shown in this paper that the probability measures generated by selfsimilar Gaussian random fields are mutually singular, whenever they have different scaling parameters. So are those generated from a selfsimilar Gaussian random field and a stationary Gaussian random field. Certain conditions are also given for the singularity of the probability measures generated from two Gaussian random fields whose covariance functions are Schoenberg-Levy kernels, and for those from stationary Gaussian random fields with spectral densities.
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Taylor & Francis
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Stochastic Analysis and Applications;v.36:no.6
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0736-2994