= Kurtz fluid limit theorem
{c}
For a <density-dependent Markov jump process> with finitely many jump vectors, bounded nonnegative rates and Lipschitz drift $F(x)=\sum_\ell\ell\beta_\ell(x)$, an initial state converging in probability to $x_0$ gives uniform convergence in probability on every finite horizon to the ODE $\dot x=F(x)$, $x(0)=x_0$. The compensated martingale has expected maximal squared size $O(N^{-1})$ by the <Doob L2 maximal inequality>; <Gronwall's inequality> transfers that estimate to the solution error.
// Target: probability-and-statistics.bigb
Back to article page
