Abstract
Palm theory on the line links two types of stationarity for marked point processes: time-stationarity and event-stationarity. The next two examples will clarify these notions. Example 7.0.1: The Renewal Process. In this type of point process, one distinguishes the delayed time-stationary version from the undelayed version whose distribution is invariant with respect to the shift that translates the first event time to the origin. We have seen that there exists a simple relation between the two versions, which are identical except for the distribution of the first event time. In the terminology of Palm theory, the undelayed version is the Palm version of the time-stationary version.
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Brémaud, P. (2020). Palm Probability on the Line. In: Point Process Calculus in Time and Space. Probability Theory and Stochastic Modelling, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-030-62753-9_7
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DOI: https://doi.org/10.1007/978-3-030-62753-9_7
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