Asymptotic theory for the detection of mixing in anomalous diffusion

Abstract

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.

References in corpus (5)

• Properties and numerical evaluation of the Rosenblatt distribution
• Codifference can detect ergodicity breaking and non-Gaussianity
• Integrated functionals of normal and fractional processes
• Fluid heterogeneity detection based on the asymptotic distribution of the time-averaged mean squared displacement in single particle tracking experiments
• The asymptotic distribution of the pathwise mean squared displacement in single particle tracking experiments