TY - JOUR
A1 - Schwarz, Wolf
A1 - Miller, Jeff O.
T1 - Locking the Wiener process to its level-crossing time
N2 - 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.
Y1 - 2010
UR - http://www.informaworld.com/smpp/section?content=a917389654&fulltext=713240928
U6 - http://dx.doi.org/10.1080/03610920902755821
SN - 0361-0926
ER -
TY - JOUR
A1 - Schwarz, Wolf
T1 - Comparing continuous and discrete birthday coincidences : "Same-Day" versus "Within 24 Hours"
N2 - In its classical form the famous birthday problem (Feller 1968; Mosteller 1987) addresses coincidences within a discrete sample space, looking at births that fall on the same calendar day. However, coincidence phenomena often arise in situations in which it is more natural to consider a continuous-time parameter. We first describe an elementary variant of the classical problem in continuous time, and then derive and illustrate close approximate relations that exist between the discrete and the continuous formulations.
Y1 - 2010
U6 - http://dx.doi.org/10.1198/tast.2009.09003
SN - 0003-1305
ER -