Counting-process intensity
= Counting-process intensity
{title2=$E(dN\mid\mathcal F_{t-})=\lambda(t)\,dt$}
A predictable intensity $\lambda(t)$ is the derivative of an absolutely continuous <compensator of a counting process>: $N(t)-\int_0^t\lambda(u)\,du$ is a <local martingale>. It represents the conditional event rate given the immediately preceding history. In <survival analysis> the individual intensity is an at-risk indicator multiplied by its <hazard function>.