A Dimension Theorem for Sample Functions of Processes with Stable Components

A Dimension Theorem for Sample Functions of Processes with Stable Components

For processes $X(t)$ with stable components we calculate $\dim X(E)$ in terms of $\dim E$, where $E$ is a fixed Borel subset of [0, 1] of known Hausdorff-Besicovitch dimension, $\dim E$. Our results extend the earlier ones of Blumenthal and Getoor in the stable case.

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Veröffentlicht in:The Annals of probability 1973-10, Vol.1 (5), p.849-853
1. Verfasser: Hendricks, W. J.
Format: Artikel
Sprache:eng
Schlagworte:
60G17
60J25
60J30
60J40
Cubes
Hausdorff dimension
Hausdorff dimensions
Mathematical functions
Mathematical theorems
Processes with stable components
Sample path properties
Short Communications
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Beschreibung
Zusammenfassung:For processes $X(t)$ with stable components we calculate $\dim X(E)$ in terms of $\dim E$, where $E$ is a fixed Borel subset of [0, 1] of known Hausdorff-Besicovitch dimension, $\dim E$. Our results extend the earlier ones of Blumenthal and Getoor in the stable case.
ISSN:0091-1798
2168-894X
DOI:10.1214/aop/1176996850