## Structural Characterization of Taboo-Stationarity for General Processes in Two-sided Time
*P. W. Glynn and H. Thorisson*
*Stochastic Processes and their Applications.* Vol. 102 (2), 311-318 (2002)
This note considers the taboo counterpart ofstationarity. A general stochastic process in
two-sided time is de.ned to be *taboo-stationary* if its global distribution does not change by
shifting the origin to an arbitrary non-random time in the future *under taboo*, that is, conditionally
on some taboo-event not having occurred up to the new time origin. The main result is
the following basic structural characterization: a process is taboo-stationary *if and only if* it can
be represented as a stochastic process with origin shifted backward in time by an independent
exponential random variable. An application to reflected Brownian motion is given. |