Abstracts
In the first part of this chapter it is shown how stochastic independence between finitely many marked point processes may be characterized in terms of the structure of the compensating measures. The last part of the chapter is devoted to the study of CPs and RCMs with independent increments (stationary or not), which are characterized as those having deterministic compensating measures, and of other stochastic processes with independent increments, with, in particular, a discussion of compound Poisson processes and more general Lévy processes.
The discussion of general Lévy processes at the end of the chapter is intended for information only and is not required reading. One may also omit reading the technical parts of the proof of Theorem 6.2.1(i) and the proof of Proposition 6.2.3(i).
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Chapter 6
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(2006). Independence. In: Point Process Theory and Applications. Probability and its Applications. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4463-6_6
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DOI: https://doi.org/10.1007/0-8176-4463-6_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4215-0
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