Simulating the Poisson Point Process

The homogeneous Poisson point process is a counting process which satisfies {N(t),t>=0} where the probability of a random variable N being equal to n at time t is Poisson-distributed. The algorithm to simulate the Poisson point process can be simplified as follows (Chen et al. 2016).

The MATLAB script for simulating multivariate homogeneous Poisson point process is given below.

Run the following command on the MATLAB console to simulate a bivariate Poisson point process with λ=5 and length=128.

X = simpoisson(2^7,2,5); 
plot(X)

Then, you have two time series as displayed below.