HITTING DISTRIBUTIONS OF α-STABLE PROCESSES VIA PATH CENSORING AND SELF-SIMILARITY

• 成果类型: Article
• 署名作者: Kyprianou, Andreas E.; Carlos Pardo, Juan; Watson, Alexander R.
• 署名单位: University of Bath; CIMAT - Centro de Investigacion en Matematicas
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP790
• 发表日期: 2014
• 页码: 398-430
• 关键词: Levy processes; recurrent extensions; explicit identities; fluctuation; 1st

摘要

We consider two first passage problems for stable processes, not necessarily symmetric, in one dimension. We make use of a novel method of path. censoring in order to deduce explicit formulas for hitting probabilities, hitting distributions and a killed potential measure. To do this, we describe in full detail the Wiener-Hopf factorization of a new Lamperti-stable-type Levy process obtained via the Lamperti transform, in the style of recent work in this area.