具有重置事件的连续时间随机游动：历史背景和新观点
Continuous-time random walks with reset events: Historical background and new perspectives
摘要：
在本文中，我们考虑一个随机过程，可能会遇到随机重置事件，重新定位系统的起始位置。我们把注意力集中在一个一维的，单调的连续时间的随机游动与恒定的漂移：该过程中移动在一个固定的方向之间的复位事件，无论是随机跳跃的效果，或通过一个确定性的偏见的行动。然而，其运动的方向在每次重新启动后随机确定。由于这些交替的动力学，有趣的特性确实出现了。一般公式的传播以及两个极端的统计，生存概率和平均首次通过时间，也来自。这些分析结果的严谨性验证了数值估计，特别是，但启发性的例子。
英文摘要：
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.
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