= Predictable compensator of a jump measure
{title2=$\mathbb E(H*N)=\mathbb E(H*\nu)\quad(H\ge0\text{ predictable})$}
The <predictable> random measure $\nu$ matching the expected <integrals> of the jump measure $N$ against every nonnegative <predictable> integrand. For displacement marks of a <Markov jump process>, $\nu(ds,dy)=K(X_{s-},dy)ds$. Multiplying the integrand by an <event> known before an <interval> proves that the compensated <integral> has conditionally centered increments; expected absolute <integrability> makes it a true <martingale>. With the compensator absolutely continuous in time, squared-integrand <integrability> gives the square-integrable compensation isometry.
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