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2015 Asymptotic behaviour of first passage time distributions for subordinators
Ronald Doney, Victor Rivero
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Electron. J. Probab. 20: 1-28 (2015). DOI: 10.1214/EJP.v20-3879

Abstract

In this paper we establish local estimates for the first passage time of a subordinator under the assumption that it belongs to the Feller class, either at zero or infinity, having as a particular case the subordinators which are in the domain of attraction of a stable distribution, either at zero or infinity. To derive these results we first obtain uniform local estimates for the one dimensional distribution of such a subordinator, which sharpen those obtained by Jain and Pruitt. In the particular case of a subordinator in the domain of attraction of a stable distribution our results are the analogue of the results obtained by the authors for non-monotone Levy processes. For subordinators an approach different to that in [6] is necessary because the excursion techniques are not available and also because typically in the non-monotone case the tail distribution of the first passage time has polynomial decrease, while in the subordinator case it is exponential.

Citation

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Ronald Doney. Victor Rivero. "Asymptotic behaviour of first passage time distributions for subordinators." Electron. J. Probab. 20 1 - 28, 2015. https://doi.org/10.1214/EJP.v20-3879

Information

Accepted: 10 September 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1333.60094
MathSciNet: MR3399827
Digital Object Identifier: 10.1214/EJP.v20-3879

Subjects:
Primary: 62E17
Secondary: 60F10, 60G51

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