Markov processes with stochastic resetting towards the origin generically converge towards 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 large deviations properties of general time-additive observables involving the position and the increments of the dynamical trajectory are then analyzed in terms of the appropriate Markov tilted processes and of the corresponding conditioned processes obtained via the generalization of Doob’s h-transform. This general formalism is described in detail 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 explicit results for the Sisyphus random walk and its variants, when the reset probabilities or reset rates are space-dependent.

对原点进行随机重置的马尔可夫过程通常收敛于非平衡稳态。因此，可以通过在水平2.5处针对经验密度和经验流的联合概率的大偏差来分析长动态轨迹，或者针对连续重置之间的偏移的经验密度通过半马尔可夫过程的大偏差来分析长动态轨迹。然后根据适当的马尔可夫倾斜过程和通过Doob的h变换的泛化获得的相应条件过程，来分析涉及时间和动态轨迹增量的一般时间可加观测量的大偏差性质。针对三种可能的框架（即离散时间/离散空间马尔可夫链）详细描述了这种一般形式主义，