 Density-dependent Markov jump process

With scale $N$, such a process has finitely many possible jump vectors $\ell /N$ occurring at rates $N{\beta }_{\ell }(x)$ depending on the current scaled state. Its drift is ${\sum }_{\ell }\ell {\beta }_{\ell }(x)$, while the predictable covariance rate of its martingale fluctuations is $N^{-1}{\sum }_{\ell }\ell {\ell }^T{\beta }_{\ell }(x)$.

// Target: probability-and-statistics.bigb