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On time- and cycle-stationarity

By Hermann Thorisson

Abstract

AbstractConsider processes split into cycles by a sequence of random times (called points). The standard Palm relationship between stationary processes with cycles and processes with stationary cycles is produced in two transparent steps: length-biasing and re-centring. It has the following standard intuitive interpretation: the process with stationary cycles behaves like the stationary one conditioned on a point at time zero. A less known modification of this relationship is produced by conditioning on the invariant σ-algebra before length-biasing. It has the following intuitive interpretation: the stationary process behaves like the cycle-stationary one centred at a time chosen at random on the line. The present approach leads to strong conditioning, limit and coupling results motivating these interpretations

Publisher: Published by Elsevier B.V.
Year: 1995
DOI identifier: 10.1016/0304-4149(94)00038-U
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