标题： 非马尔可夫随机游走的占用时间统计 显示英文标题

标题： Occupation time statistics for non-Markovian random walks

摘要： 我们研究基于连续时间随机游走广义主方程形式的非马尔可夫随机行走者的占据时间统计。 我们还探讨了随机行走者额外经历随机重置动力学的情况。 我们推导并求解了后向费曼-卡奇方程，以找到区间内占据时间以及半无限域内半占据时间的特征函数。 我们分析了当基础随机游走为正常或异常时，两种占据时间的PDFs、矩、极限分布和遍历性。 对于半占据时间，我们重新审视著名的弧线定律，并检验其在行走者休息期各种区域内的有效性。 我们的结果已通过数值模拟验证，显示出极好的一致性。 显示英文摘要

摘要： We study the occupation time statistics for non-Markovian random walkers based on the formalism of the generalized master equation for the Continuous-Time Random Walk. We also explore the case when the random walker additionally undergoes a stochastic resetting dynamics. We derive and solve the backward Feynman-Kac equation to find the characteristic function for the occupation time in an interval and for the half occupation time in the semi-infinite domain. We analyze the behaviour of the PDFs, the moments, the limiting distributions and the ergodic properties for both occupation times when the underlying random walk is normal or anomalous. For the half occupation time, we revisit the famous arcsine law and examine its validity pertaining to various regimes of the rest period of the walker. Our results have been verified with numerical simulations exhibiting an excellent agreement.