English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Density-dependent Markov chains form an important class of continuous-timeMarkov chains in population dynamics. On any fixed time window [0, T ], whenthe scale parameter K > 0 is large such chains are well approximated by thesolution of an ODE (the fluid limit), with Gaussian fluctuations superimposedupon it. In this paper we quantify the period of time during which thisGaussian approximation remains precise, uniformly on the trajectory, in thecase where the fluid limit converges to an exponentially stable equilibriumpoint. We provide a new coupling between the density-dependent chain and theapproximating Gaussian process, based on a construction of Kurtz using thecelebrated Koml{\'o}s-Major-Tusn{\'a}dy theorem for random walks. We show thatunder mild hypotheses the time T(K) necessary for the strong approximationerror to reach a threshold $\epsilon$(K)<<1 is at least of order exp(V K$\epsilon$(K)), for some constant V > 0. This notably entails that the Gaussianapproximation yields the correct asymptotics regarding the time scales ofmoderate deviations. We also present applications to the Gaussian approximationof the logistic birth-and-death process conditioned to survive, and to theestimation of a quantity modeling the cost of an epidemic.

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