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