The packing measure of a general subordinator

Bert E. Fristedt, S. James Taylor

Research output: Contribution to journalArticlepeer-review

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Abstract

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 subordinator X(t) is equivalent to the upper local growth problem for Y(t)=min (Y1(t), Y2(t)), where Y1 and Y2 are independent copies of X. 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 of Y (although, as is well known, there is no such function for the subordinator X itself).

Original languageEnglish (US)
Pages (from-to)493-510
Number of pages18
JournalProbability Theory and Related Fields
Volume92
Issue number4
DOIs
StatePublished - Dec 1 1992

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