Large deviations for Markov processes with stochastic resetting : analysis via the empirical density and flows or via excursions between resets

Cecile Monthus

Published 2020-09-25Version 1

Markov processes with stochastic resetting towards the origin produce non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at level 2.5 for the joint probability of the empirical density and the empirical flows, or via the large deviations of semi-Markov processes for the empirical density of excursions between consecutive resets. The general formalism is described for the three possible frameworks, namely discrete-time/discrete-space Markov chains, continuous-time/discrete-space Markov jump processes, and continuous-time/continuous-space diffusion processes, and is illustrated with examples based on the Sisyphus Random Walk.