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2014 On the range of subordinators
Mladen Savov
Author Affiliations +
Electron. Commun. Probab. 19: 1-10 (2014). DOI: 10.1214/ECP.v19-3629

Abstract

In this note we look into detail into the box-counting dimension of subordinators. Given that X is a non-decreasing Levy process which is not Compound Poisson process we show that in the limit, a.s., the minimum number of boxes of size $a$ that cover the range of $(X_s)_{s\leq t}$ is a.s. of order $t/U(a)$, where U is the potential function of X. This is a more rened result than the lower and upper index of the box-counting dimension computed by Jean Bertoin in his 1999 book, which deals with the asymptotic of the number of boxes at logarithmic scale.

Citation

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Mladen Savov. "On the range of subordinators." Electron. Commun. Probab. 19 1 - 10, 2014. https://doi.org/10.1214/ECP.v19-3629

Information

Accepted: 11 December 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60127
MathSciNet: MR3291621
Digital Object Identifier: 10.1214/ECP.v19-3629

Subjects:
Primary: 60J75
Secondary: 60K99

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