In this paper, we develop asymptotic theory for the mixing detection methodology proposed by Magdziarz and Weron [Phys. Rev. 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.

中文翻译：

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异常扩散中混合检测的渐近理论

在本文中，我们为 Magdziarz 和 Weron 提出的混合检测方法开发了渐近理论 [Phys. 修订版 E 84 , 051138 (2011)]。这些假设涵盖了广泛的高斯随机过程系列，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率可能分别是高斯或非高斯和标准或非标准，具体取决于扩散指数。结果为基于单一观察样本路径和稳健假设检验的混合检测铺平了道路。