= Poisson concentration proof of a density-dependent fluid limit
{c}
{title2=$Z^n(t)=Z^n(0)+\sum_jv_j\,N_j(n\int_0^t\beta_j(Z^n(u))\,du)/n$}
If the rate functions are bounded and <Lipschitz> on an invariant compact state space, the <Poisson time-change representation of a Markov chain> has drift $F=\sum_jv_j\beta_j$. Each centered Poisson term is uniformly small after division by $n$. The <Gronwall inequality> then bounds the distance to $\dot z=F(z)$ by the initial error and the centered counting error, multiplied by $e^{LT}$. A Poisson maximal concentration bound gives exponentially decreasing error probabilities for a fixed horizon and fixed error tolerance.
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