Occupation time statistics of the fractional Brownian motion in a finite domain

Occupation time statistics of the fractional Brownian motion in a finite domain
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有限域分数布朗运动的占用时间统计

DOI：
10.1103/physreve.106.064132
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发表时间：
2022
期刊：
Phys. Rev. E
影响因子：
--
通讯作者：
Mutsumi Kimura and Takuma Akimoto
Mutsumi Kimura and Takuma Akimoto
中科院分区：
--
文献类型：
--
作者：
坂元啓紀;糸井千岳;G. Kato;糸井千岳;Mutsumi Kimura and Takuma Akimoto

文献摘要

相似文献

研究了一类非马尔可夫过程的典型模型--分数布朗运动（fBm）的占据时间的统计特性。由于非马尔可夫性质，到原点的递归时间取决于历史。数值模拟表明，对连续递归时间的总和的依赖变得很弱。结果，当fBm的Hurst指数接近1/2时，在有限区域中的占据时间的分布遵循Mittag-Leffler分布。我们展示了更新理论的时间平均观测值的分布行为。这个结果是一般马尔可夫过程中的分布极限定理（称为Darling-Kac定理）到非马尔可夫过程的推广。
We study statistics of occupation times for a fractional Brownian motion (fBm), which is a typical model of a non-Markov process. Due to the non-Markovian nature, recurrence times to the origin depend on the history. Numerical simulations indicate that dependence on the sum of successive recurrence times becomes weak. As a result, the distribution of the occupation time in a finite domain follows the Mittag-Leffler distribution when the Hurst exponent of the fBm is close to 1/2. We show this distributional behavior of a time-averaged observable by renewal theory. This result is an extension of the distributional limit theorem known as the Darling-Kac theorem in general Markov processes to non-Markov processes.