Extreme first passage times of piecewise deterministic Markov processes
Extreme first passage times of piecewise deterministic Markov processes
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DOI：
10.1088/1361-6544/abcb07
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发表时间：
2021-05-01
期刊：
影响因子：
1.7
通讯作者：
Lawley, Sean D.
中科院分区：
文献类型：
--
作者：
Lawley, Sean D.
N 1个搜索者中最快的搜索者找到目标所需的时间决定了许多物理、化学和生物过程的时间尺度。这个时间被称为极端首次通过时间（FPT），通常比单个双稳态的FPT快得多。扩散的极端FPT已经研究了几十年，但对其他类型的随机过程知之甚少。本文研究了分段确定马尔可夫过程的极值FPT的分布。PDMP是一类广泛的随机过程，在随机事件之间确定性地演化。利用经典的极值理论，我们证明了一般定理，产生的分布和矩的极端FPT的极限在许多搜索的基础上的FPT的短期分布的单个搜索者。然后，我们将这些定理应用到一些典型的PDMP，包括运行和翻滚搜索在一个，两个和三个空间维度。我们讨论了我们的结果的背景下，一些生物系统，并显示我们的方法占一个非物理性质的扩散，这可能是极端的统计问题。
The time it takes the fastest searcher out of N 1 searchers to find a target determines the timescale of many physical, chemical, and biological processes. This time is called an extreme first passage time (FPT) and is typically much faster than the FPT of a single searcher. Extreme FPTs of diffusion have been studied for decades, but little is known for other types of stochastic processes. In this paper, we study the distribution of extreme FPTs of piecewise deterministic Markov processes (PDMPs). PDMPs are a broad class of stochastic processes that evolve deterministically between random events. Using classical extreme value theory, we prove general theorems which yield the distribution and moments of extreme FPTs in the limit of many searchers based on the short time distribution of the FPT of a single searcher. We then apply these theorems to some canonical PDMPs, including run and tumble searchers in one, two, and three space dimensions. We discuss our results in the context of some biological systems and show how our approach accounts for an unphysical property of diffusion which can be problematic for extreme statistics.