Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7550434 | Stochastic Processes and their Applications | 2018 | 19 Pages |
Abstract
Let {X(t):tâRd} 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):tâRd}=d{cDX(t):tâRd} for all c>0, where E is a dÃd real matrix and D is an mÃm 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.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Ercan Sönmez,