| Autor: |
Kern, Peter, Pleschberger, Leonard |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We explicitly calculate the Hausdorff dimension of the graph and range of an isotropic stable L\'{e}vy process $X$ plus deterministic drift function $f$. For that purpose we use a restricted version of the genuine Hausdorff dimension which is called the parabolic Hausdorff dimension. It turns out that covers by parabolic cylinders are optimal for treating self-similar processes, since their distinct non-linear scaling between time and space geometrically matches the self-similarity of the processes. We provide explicit formulas for the Hausdorff dimension of the graph and the range of $X+f$. In sum the parabolic Hausdorff dimension of the drift term $f$ alone contributes to the Hausdorff dimension of $X+f$. Further, we derive some formulas and bounds for the parabolic Hausdorff dimension. |
| Databáze: |
arXiv |
| Externí odkaz: |
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