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Markov processes with stochastic resetting towards the origin genericallyconverge towards non-equilibrium steady-states. Long dynamical trajectories canbe thus analyzed via the large deviations at Level 2.5 for the jointprobability of the empirical density and the empirical flows, or via the largedeviations of semi-Markov processes for the empirical density of excursionsbetween consecutive resets. The large deviations properties of generaltime-additive observables involving the position and the increments of thedynamical trajectory are then analyzed in terms of the appropriate Markovtilted processes and of the corresponding conditioned processes obtained viathe generalization of Doob's h-transform. This general formalism is describedin detail for the three possible frameworks, namelydiscrete-time/discrete-space Markov chains, continuous-time/discrete-spaceMarkov jump processes and continuous-time/continuous-space diffusion processes,and is illustrated with explicit results for the Sisyphus Random Walk and itsvariants, when the reset probabilities or reset rates are space-dependent.

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