论文标题
通过随机重置的向后和向前扩散的时间：一种更新理论方法
Conditioned backward and forward times of diffusion with stochastic resetting: a renewal theory approach
论文作者
论文摘要
随机重置自然可以理解为续签基础随机过程的演变的续签过程。在这项工作中，我们从更新理论的角度正式得出了通过重置的扩散结果。与更新理论的概念平行，我们为随机过程引入了条件的向后和向前时间，鉴于系统的当前状态已知，因此重置为自上次和下一个重置以来的时代。我们专注于研究马尔可夫和非马克维亚重置下的扩散。在这些情况下，我们发现有条件的后和正向时间PDF，将它们与该过程的数值模拟进行了比较。特别是，我们发现，对于具有渐近形式$φ（t）\ sim t^{ - 1-1-α} $的幂律重置时间PDF，条件向后和向前时间的属性发生了重大变化，以$α$的半数为单位。这是由于扩散$ p（x，t）\ sim 1/\ sqrt {t} $与重置时间pdf之间的长期缩放缩放之间的组成。
Stochastic resetting can be naturally understood as a renewal process governing the evolution of an underlying stochastic process. In this work, we formally derive well-known results of diffusion with resets from a renewal theory perspective. Parallel to the concepts from renewal theory, we introduce the conditioned backward and forward times for stochastic processes with resetting to be the times since the last and until the next reset, given that the current state of the system is known. We focus on studying diffusion under Markovian and non-Markovian resetting. For these cases, we find the conditioned backward and forward time PDFs, comparing them with numerical simulations of the process. In particular, we find that for power-law reset time PDFs with asymptotic form $φ(t)\sim t^{-1-α}$, significant changes in the properties of the conditioned backward and forward times happen at half-integer values of $α$. This is due to the composition between the long-time scaling of diffusion $P(x,t)\sim 1/\sqrt{t}$ and the reset time PDF.
