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The packing measure of a general subordinator
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  • Published: December 1992

The packing measure of a general subordinator

  • Bert E. Fristedt1 &
  • S. James Taylor2 

Probability Theory and Related Fields volume 92, pages 493–510 (1992)Cite this article

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  • 13 Citations

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Summary

Precise conditions are obtained for the packing measure of an arbitrary subordinator to be zero, positive and finite, or infinite. It develops that the packing measure problem for a subordinatorX(t) is equivalent to the upper local growth problem forY(t)=min (Y 1 (t), Y 2 (t)), whereY 1 andY 2 are independent copies ofX. A finite and positive packing measure is possible for subordinators “close to Cauchy”; for such a subordinator there is non-random concave upwards function that exactly describes the upper local growth ofY (although, as is well known, there is no such function for the subordinatorX itself).

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References

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA

    Bert E. Fristedt

  2. Department of Mathematics, University of Virginia, 22903, Charlottesville, VA, USA

    S. James Taylor

Authors
  1. Bert E. Fristedt
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  2. S. James Taylor
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Additional information

Research supported in part by NSF under contracts (1) DMS 87-01866, and (2) DMS 87-01212

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Fristedt, B.E., Taylor, S.J. The packing measure of a general subordinator. Probab. Th. Rel. Fields 92, 493–510 (1992). https://doi.org/10.1007/BF01274265

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  • Received: 07 January 1991

  • Revised: 28 November 1991

  • Issue Date: December 1992

  • DOI: https://doi.org/10.1007/BF01274265

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Precise Condition
  • Measure Problem
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