Sep 18, 2017

DECOMPOSITION OF A POISSON STREAM IS POISSON: CONSIDER A POISSON PROCESS X WITH PARAMETER Λ…

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Decomposition of a Poisson stream is Poisson: consider a Poisson process X with parameter λ that is decomposed into k separate Poisson streams X j, j = 1, 2,…, k. The decomposition is such that

Conditioning on n, the number of arrivals in the original stream up to some time t, show first that

which shows that the k decomposed streams are indeed Poisson processes with parameters λpj.


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