Solution (source code)

= Solution

The <cumulative hazard function> is defined through the conditional mean increment
$$
\mathbb E\{dN(t)\mid Y(t)=y(t)\}=y(t)\,dH(t).
$$
Equivalently, $dH(t)=\mathbb E\{dN(t)\mid Y(t)=1\}$ and $H(t)=\int_0^tdH(u)$.