Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment
Abstract
The large deviations at level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasistationary states in terms of their empirical timeaveraged density and of their timeaveraged empirical flows over a large timewindow T. The standard spectral problem for the slowest relaxation mode can be recovered from the full optimization of the extinction rate over all these empirical observables and the equivalence can be understood via the Doob generator of the process conditioned to survive up to time T. The large deviation properties of any timeadditive observable of the Markov trajectory before extinction can be derived from the level 2.5 via the decomposition of the timeadditive observable in terms of the empirical density and the empirical flows. This general formalism is described for continuoustime Markov chains, with applications to population birthdeath model in a stable or in a switching environment, and for diffusion processes in dimension d.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 January 2022
 DOI:
 10.1088/17425468/ac4519
 arXiv:
 arXiv:2107.05354
 Bibcode:
 2022JSMTE2022a3206M
 Keywords:

 absorbing states;
 large deviations in nonequilibrium systems;
 metastable states;
 stochastic processes;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 v2 : 25 pages (corrected typos + new comment on the application to other types of metastable states+added references)