Large Deviations for dynamical fluctuations of Open Markov processes, with application to random cascades on trees
Abstract
The large deviations at 'Level 2.5 in time' for time-dependent ensemble-empirical-observables, introduced by C. Maes, K. Netocny and B. Wynants [Markov Proc. Rel. Fields. 14, 445 (2008)] for the case of independent Markov jump processes, are extended to the case of open Markov processes with reservoirs : explicit formulas are given for the joint probability of empirical occupation numbers and empirical flows, both for discrete-time dynamics and for continuous-time jump dynamics, with possibly time-dependent dynamical rules and/or time-dependent driving of the reservoirs. This general formalism is then applied to random cascades on trees, where particles are injected at the root via a 'source reservoir', while the particles are removed at the leaves of the last generation of the tree via 'sink reservoirs'.
Cite
@article{arxiv.1808.09703,
title = {Large Deviations for dynamical fluctuations of Open Markov processes, with application to random cascades on trees},
author = {Cecile Monthus},
journal= {arXiv preprint arXiv:1808.09703},
year = {2021}
}
Comments
v2=revised version with new discussions in the text and new Appendix (21 pages)