Structural characterization of taboo-stationarity for general processes in two-sided time

Peter W. Glynn and Hermann Thorisson

Stochastic Processes and their Applications, 2002, vol. 102, issue 2, 311-318

Abstract: This note considers the taboo counterpart of stationarity. A general stochastic process in two-sided time is defined 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.

Keywords: Quasi-stationarity (search for similar items in EconPapers)
Date: 2002
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