论文标题
Markov过程的大偏差，具有随机重置：通过经验密度和流动分析或通过重置之间的偏移
Large deviations for Markov processes with stochastic resetting : analysis via the empirical density and flows or via excursions between resets
论文作者
论文摘要
Markov随机重置向原点的过程会汇聚到非平衡稳态。因此，对于经验密度和经验流的关节概率，可以通过较大的偏差在2.5级的大偏差中分析长的动力轨迹，或者通过半马多夫过程的大偏差，以实现连续复位之间的经验密度的经验密度。然后，通过适当的Markov倾斜过程以及通过DOOB的H-Transantform的概括来分析涉及位置和动力学轨迹的增量的一般时间添加可观察到的大偏差属性。三个可能的框架详细描述了这种一般形式主义，即离散的时间/离散空间马尔可夫链，连续/离散空间马尔可夫跳跃过程以及连续/连续/连续的空间扩散过程，并通过sisyphus随机步行及其变体的明确结果进行了明确的结果，当时是空间差异的率，均具有空间差异。
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.
