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The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields

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  • Sönmez, Ercan

Abstract

Let {X(t):t∈Rd} be a multivariate operator-self-similar random field with values in Rm. Such fields were introduced in [22] and satisfy the scaling property {X(cEt):t∈Rd}=d{cDX(t):t∈Rd} for all c>0, where E is a d×d real matrix and D is an m×m real matrix. We solve an open problem in [22] by calculating the Hausdorff dimension of the range and graph of a trajectory over the unit cube K=[0,1]d in the Gaussian case. In particular, we enlighten the property that the Hausdorff dimension is determined by the real parts of the eigenvalues of E and D as well as the multiplicity of the eigenvalues of E and D.

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  • Sönmez, Ercan, 2018. "The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 426-444.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:2:p:426-444
    DOI: 10.1016/j.spa.2017.05.003
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