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Hausdorff Dimension of Operator Stable Sample Paths

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Abstract.

The Hausdorff dimension of the sample paths of a stochastic process with stationary independent operator stable increments is computed. With probability one, every sample path has the same dimension, depending on the real parts of the eigenvalues of the operator stable exponent.

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Authors and Affiliations

  1. University of Dortmund, Germany, , , , , , DE

    Peter Becker-Kern & Hans-Peter Scheffler

  2. University of Nevada, Reno, USA, , , , , , US

    Mark M. Meerschaert

Authors
  1. Peter Becker-Kern
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  2. Mark M. Meerschaert
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  3. Hans-Peter Scheffler
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Additional information

Received May 28, 2002; in revised form October 2, 2002 Published online May 15, 2003

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Becker-Kern, P., Meerschaert, M. & Scheffler, HP. Hausdorff Dimension of Operator Stable Sample Paths. Monatsh. Math. 140, 91–101 (2003). https://doi.org/10.1007/s00605-002-0534-8

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  • DOI: https://doi.org/10.1007/s00605-002-0534-8

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