Asymptotic behaviour of first passage time distributions for subordinators

作者：Doney Ronald A^*; Rivero Victor M

来源：Electronic Journal of Probability, 2015, 20(0): 1-28.

DOI：10.1214/EJP.v20-3879

• Subordinators
• first passage time distribution
• local limit theorems
• Feller class

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 [9]. 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 in [5] for non-monotone Levy processes. For subordinators an approach different to that in [5] 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.

• 出版日期2015-9-10