Talk:Campbell's theorem (probability)
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Different Campbell's theorems
Campbell's theorem comes in a few forms, so I'll cite the one from Kingman's book (for Poisson processes), then give the more general Campbell's theorem/formula (for general point processes). I will put the more general formula first since it is, well, more general, and leads to more general formulas and theorems such as Campbell-Mecke theorems and Palm calculus results, which may be incorporate later into this article.Improbable keeler (talk) 21:26, 17 November 2015 (UTC)
Neuroscience application?
I definitely believe that Campbell's theorem (or shot noise) is used in neuroscience, but I need a reference. Also, is it necessary to state when and where higher moments (for which process, incidentally) were done? Improbable keeler (talk) 21:26, 17 November 2015 (UTC)
Neuroscience
The total input
Extension to higher moments is given in.[1]
Another common extension is to consider a sum with random amplitudes
In this case the cumulants of equal
where are the raw moments of the distribution of .
References
- ^ S.O. Rice Mathematical analysis of random noise Bell Syst. Tech. J. 24, 1944 reprinted in "'Selected papers on noise and random processes N. Wax (editor) Dover 1954.