# Simulating a (discretized) Cox process via binomial sampling

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.