ON THE INVERSE FIRST-PASSAGE-TIME PROBLEM FOR A WIENER PROCESS

• 成果类型: Article
• 署名作者: Zucca, Cristina; Sacerdote, Laura
• 署名单位: University of Turin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP571
• 发表日期: 2009
• 页码: 1319-1346
• 关键词: probability densities; integral-equation; brownian-motion; BOUNDARIES

摘要

The inverse first-passage problem for a Wiener process (W(t))(t >= 0) seeks to determine a function b : R(+) -> R such that tau = inf{t > 0 vertical bar W(t) >= b(t)} has a given law. In this paper two methods for approximating the unknown function b are presented. The errors of the two methods are studied. A set of examples illustrates the methods. Possible applications are enlighted.