Density-dependent Markov jump process
= 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 process>[predictable] <covariance> rate of its <martingale> fluctuations is $N^{-1}\sum_\ell\ell\ell^T\beta_\ell(x)$.
// Target: probability-and-statistics.bigb