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Let X be a Cox process (doubly-stochastic Poisson process) with fixed intensity(rate) $\lambda=50$ , and choose some small time interval $dt=0.01$ . Is the proper way to simulate this, by letting Y be a binomial distribution with the number of trials equal to $n=1$ and the probability equal to $p=dt*\lambda$ and then drawing from $Y$ to populate each element of the time-discretized grid $x=[0..dt,dt..dt*2,dt*2..dt*3,..] ?

There is an additional stipulation here, that the variable $dt$ must be chosen small enough such that $p<1$

http://people.math.aau.dk/~rw/Papers/cox2.RR.ps seems to be a good reference on Cox process inference.

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