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


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.


Download Citation

Ronald Doney. Victor Rivero. "Asymptotic behaviour of first passage time distributions for subordinators." Electron. J. Probab. 20 1 - 28, 2015.


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

Primary: 62E17
Secondary: 60F10, 60G51


Vol.20 • 2015
Back to Top