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Reading Wikipedia articles for Cox point process and Poisson random measure, I was wondering if they are actually the same concept?

If they are not, I wonder how to understand the concept for Cox point process?

Thanks!

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    More precisely, the latter, as stated in the link, is for a measure space with $\sigma$-finite measure $\mu$; the same should be true for the former upon replacing "point process" with "random measure". The essential difference is that the random measure in the former is, in general, random itself ("doubly stochastic").2011-04-27

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