论文标题
渐近理论用于检测异常扩散中混合的理论
Asymptotic theory for the detection of mixing in anomalous diffusion
论文作者
论文摘要
在本文中，我们开发了M. M. M. M. M. M. M. M. M. M. M. M. M. M. M. M. and Review E，84：051138（2011）]提出的混合检测方法的渐近理论。这些假设涵盖了一个广泛的高斯随机过程，包括分数高斯噪声和分数Ornstein-Uhlenbeck过程。我们表明，检测统计量的渐近分布和收敛速率分别可能是高斯或非高斯和标准或非标准的，具体取决于扩散指数。结果为基于单个观察到的样本路径和可靠的假设检验而混合检测的方式铺平了道路。
In this paper, we develop asymptotic theory for the mixing detection methodology proposed by M. Magdziarz and A. Weron [Physical Review E, 84:051138 (2011)]. The assumptions cover a broad family of Gaussian stochastic processes including fractional Gaussian noise and the fractional Ornstein-Uhlenbeck process. We show that the asymptotic distribution and convergence rates of the detection statistic may be, respectively, Gaussian or non-Gaussian and standard or nonstandard depending on the diffusion exponent. The results pave the way for mixing detection based on a single observed sample path and by means of robust hypothesis testing.
