Considering intensity as a stochastic variable

Up to now, we have considered intensity as a fixed parameter of either:

• the whole study region $A$ (homogeneous poisson process):

$$\lambda = \frac{E[N(A)]}{|A|}$$

• the location $x$ (inhomogeneous poisson process):

$$\lambda(x) = \lim\limits_{|dx| \to 0}\frac{E[N(dx)]}{|dx|}$$