论文标题
马尔可夫重置在有限域中的非标准扩散
Non-standard diffusion under Markovian resetting in bounded domains
论文作者
论文摘要
我们考虑一个步行者以一维间隔移动，并在马尔可夫安置到初始位置的影响下具有吸收边界。步行者的运动遵循随机步行，其特征是连续短跳之间进行一般的等待时间分布。我们根据等待时间概率的统计属性，研究了最佳复位率的存在，该速率的最佳复位速率将平均出口通过时间最小化。将先前的结果推广到马尔可夫随机步行中，我们在这里发现，取决于等待时间概率的相对标准偏差的值，重置可以是（i）永远不会有益，（ii）有益，取决于重置到边界的距离，或（iii）总是有益的。
We consider a walker moving in a one-dimensional interval with absorbing boundaries under the effect of Markovian resettings to the initial position. The walker's motion follows a random walk characterized by a general waiting time distribution between consecutive short jumps. We investigate the existence of an optimal reset rate, which minimizes the mean exit passage time, in terms of the statistical properties of the waiting time probability. Generalizing previous results restricted to Markovian random walks, we here find that, depending on the value of the relative standard deviation of the waiting time probability, resetting can be either (i) never beneficial, (ii) beneficial depending on the distance of the reset to the boundary, or (iii) always beneficial.
