In Section 3.4 we gave a brief introduction to Palm-Khinchin equations and noted that, for a stationary point process on the line, they provide a link between counting and interval properties. In this chapter we study this link both in more detail and in a more general setting. It is a topic that continues to find new applications, both within point process theory itself, and in the applications of that theory to ergodic theory, queueing theory, stochastic geometry and many other fields. Its continuing relevance is linked to the shift of viewpoint that it entails: from an absolute frame of reference outside the process under study, to a frame of reference inside the process (meaning, for a point process, relative to a point of the process). Such a change of viewpoint is usually insightful, and sometimes essential, in seeking an understanding of point process properties.


Fractal Dimension Point Process Random Measure Ergodic Theorem Moment Measure 
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© Springer 2008

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