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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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    The latter is a special case, as one can conclude from the paragraph starting with "It is easy to see that..." in the first link (consider the inhomogeneous case).2011-04-27
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    More precisely, the latter is essentially a special case... (consider $\mathbb{R}^d$).2011-04-27
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    @Shai: Thanks! From the links, it seems the latter (Poisson random measure) is for a general measure space not just $\mathbb{R}^d$, while the former (Cox point process) although not specified is perhaps for $\mathbb{R}^d$. Right?2011-04-27
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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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