Locking the Wiener process to its level-crossing time
- We consider the specific transformation of a Wiener process {X(t), t >= 0} in the presence of an absorbing barrier a that results when this process is "time-locked" with respect to its first passage time T-a through a criterion level a, and the evolution of X(t) is considered backwards ( retrospectively) from T-a. Formally, we study the random variables defined by Y(t) = X(T-a - t) and derive explicit results for their density and mean, and also for their asymptotic forms. We discuss how our results can aid interpretations of time series "response-locked" to their times of crossing a criterion level.
| Author details: | Wolfgang SchwarzORCiDGND, Jeff O. Miller |
|---|---|
| URL: | http://www.informaworld.com/smpp/section?content=a917389654&fulltext=713240928 |
| DOI: | https://doi.org/10.1080/03610920902755821 |
| ISSN: | 0361-0926 |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2010 |
| Publication year: | 2010 |
| Release date: | 2017/03/25 |
| Source: | Communications in statistics-theory and methods. - ISSN 0361-0926. - 39 (2010), 2, S. 372 - 381 |
| Organizational units: | Humanwissenschaftliche Fakultät / Strukturbereich Kognitionswissenschaften / Department Psychologie |
| Peer review: | Referiert |
| Institution name at the time of the publication: | Humanwissenschaftliche Fakultät / Institut für Psychologie |
