I saw in a paper that the autocorrelation function of a poissonian point process is the following, R(t)=v^2+v*delta(t), written in Matlab style. The t is the lag of the autocorrelation, v is the intensity of the (homogeneous)poissonian process and delta is the delta function. My first question is how to prove it.

I was trying to follow a proof of this at http://icwww.epfl.ch/~gerstner/SPNM/node34.html#SECTION02425100000000000000

but I did not figure out where coefficient 1/2 1/3 1/4 etc are from, for the summation in Equ. 5.37. It was obvious though that this would give a Taylor expansion of an exponential.

Please also show me any alternative proofs.

My second question is, what is the the autocorrelation function of the inhomogeneous poisson point process, and how to prove it.

I was trying to follow a proof of this at http://icwww.epfl.ch/~gerstner/SPNM/node34.html#SECTION02425100000000000000

but I did not figure out where coefficient 1/2 1/3 1/4 etc are from, for the summation in Equ. 5.37. It was obvious though that this would give a Taylor expansion of an exponential.

Please also show me any alternative proofs.

My second question is, what is the the autocorrelation function of the inhomogeneous poisson point process, and how to prove it.

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