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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.

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Author:Wolf Schwarz, Jeff O. Miller
Document Type:Article
Year of first Publication:2010
Year of Completion: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 / Institut für Psychologie
Peer Review:Referiert