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.