Strong Gaussian approximation of metastable density-dependent Markov chains on large time scales

We consider density-dependent Markov chains converging, as the scale parameter K>0 goes to infinity, solution of an ODE admitting exponentially stable equilibrium point. provide a new strong approximation density by Gaussian process, based on construction Kurtz using Komlós–Major–Tusnády theorem. show that given any threshold ?(K)?1 greater than multiple log(K)/K, time error needs reach ?(K) is at least order exp(VK?(K)), for some V>0. discuss consequences moderate deviations, applications logistic birth-and-death process conditioned survive and epidemic model.