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The packing measure of a general subordinator. (English) Zbl 0767.60009
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 subordinator \(X(t)\) is equivalent to the upper local growth problem for \(Y(t)=\min(Y_ 1(t),Y_ 2(t))\), where \(Y_ 1\) and \(Y_ 2\) 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).

MSC:
60D05 Geometric probability and stochastic geometry
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