 Compensator of a counting process

The compensator of a counting process $N(t)$ is a predictable increasing process $\Lambda (t)$ such that $N(t)-\Lambda (t)$ is a local martingale. For an observed event process with at-risk process $Y(t)$ and hazard function $h(t)$, it is $\Lambda (t)={\int }_0^{t}Y(u)h(u)du$ under independent censoring. It is cumulative intensity, rather than an event probability.