Asymptotic behaviour of first passage time distributions for Levy processes

• 成果类型: Article
• 署名作者: Doney, R. A.; Rivero, V.
• 署名单位: University of Manchester
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0448-x
• 发表日期: 2013
• 页码: 1-45
• 关键词: random-walks

摘要

Let be a real valued L,vy process that is in the domain of attraction of a stable law without centering with norming function As an analogue of the random walk results in Vatutin and Wachtel (Probab Theory Relat Fields 143(1-2):177-217, 2009) and Doney (Probab Theory Relat Fields 152(3-4):559-588, 2012), we study the local behaviour of the distribution of the lifetime under the characteristic measure of excursions away from of the process reflected in its past infimum, and of the first passage time of below under for in two different regimes for viz. and for some We sharpen our estimates by distinguishing between two types of path behaviour, viz. continuous passage at and discontinuous passage. In order to prove our main results we establish some sharp local estimates for the entrance law of the excursion process associated to reflected in its past infimum.