On the inverse first-passage-time problem for a Wiener process

The inverse first-passage problem for a Wiener process (Wt)t.0 seeks to determine a function b: .+.. such that .=inf{t>0|Wt.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. Citation Download Citation Cristina Zucca. Laura Sacerdote. "On the inverse first-passage-time problem for a Wiener process." Ann. Appl. Probab. 19 (4) 1319 - 1346, August 2009. https://doi.org/10.1214/08-AAP571