Analytic crossing probabilities for certain barriers by Brownian motion

• 成果类型: Article
• 署名作者: Kahale, Nabil
• 署名单位: heSam Universite; ESCP Business School
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP488
• 发表日期: 2008
• 页码: 1424-1440
• 关键词: boundary; tests; drift; time

摘要

We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval [0, T] via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class of barriers on [0, T] by proving a Schwartz distribution version of the method of images. Analytic expressions for crossing probabilities and related densities are given for new explicit and semi-explicit barriers.