Aging arcsine law in Brownian motion and its generalization
Aging arcsine law in Brownian motion and its generalization
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布朗运动中的老化反正弦定律及其推广
DOI：
10.1103/physreve.102.032103
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发表时间：
2020
影响因子：
2.4
通讯作者：
Yano Kouji
中科院分区：
文献类型：
--
作者：
Akimoto Takuma;Sera Toru;Yamato Kosuke;Yano Kouji
经典的反正弦定律指出，布朗运动中占据时间在正侧或负侧的分数并不收敛于常数，而是在分布上收敛于反正弦分布。在这里，我们考虑系统的准备如何影响反正弦定律，即，反正弦定律的老化。我们推导出了布朗运动中占据时间统计的一个老化分布定理，其中测量开始时间与测量时间的比值在确定分布的形状中起着重要的作用。此外，我们证明了这个结果可以推广为更新过程中的年龄分布极限定理。
Classical arcsine law states that the fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here we consider how a preparation of the system affects the arcsine law, i.e., aging of the arcsine law. We derive an aging distributional theorem for occupation time statistics in Brownian motion, where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution. Furthermore, we show that this result can be generalized as an aging distributional limit theorem in renewal processes.