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):

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