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

Adrien Prodhomme

Stochastic Processes and their Applications, 2023, vol. 160, issue C, 218-264

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

Keywords: Density-dependent Markov chains; Strong approximation; Gaussian approximation; Metastability (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2023.01.018

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