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

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  • Glynn, Peter W.
  • Thorisson, Hermann

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.

Suggested Citation

  • Glynn, Peter W. & Thorisson, Hermann, 2002. "Structural characterization of taboo-stationarity for general processes in two-sided time," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 311-318, December.
    • Handle: RePEc:eee:spapps:v:102:y:2002:i:2:p:311-318
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    1. Glynn, Peter W. & Thorisson, Hermann, 2001. "Two-sided taboo limits for Markov processes and associated perfect simulation," Stochastic Processes and their Applications, Elsevier, vol. 91(1), pages 1-20, January.
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      Keywords

      Quasi-stationarity;

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