31462
2010
2010
eng
article
1
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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.
http://www.informaworld.com/smpp/section?content=a917389654&fulltext=713240928
10.1080/03610920902755821
0361-0926
allegro:1991-2014
10107757
Communications in statistics-theory and methods. - ISSN 0361-0926. - 39 (2010), 2, S. 372 - 381
Wolf Schwarz
Jeff O. Miller
Institut für Psychologie
Referiert
12502
2010
2010
eng
article
1
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Comparing continuous and discrete birthday coincidences : "Same-Day" versus "Within 24 Hours"
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.
10.1198/tast.2009.09003
0003-1305
allegro:1991-2014
10107756
American statistician. - ISSN 0003-1305. - 64 (2010), 1, S. 34 - 36
Wolf Schwarz
Institut für Psychologie
Referiert