@article{SchwarzMiller2010,
  author    = {Schwarz, Wolfgang and Miller, Jeff O.},
  title     = {Locking the Wiener process to its level-crossing time},
  issn      = {0361-0926},
  doi       = {10.1080/03610920902755821},
  year      = {2010},
  abstract  = {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.},
  language  = {en}
}