Asymptotic theory for the detection of mixing in anomalous diffusion
- 1 June 2021
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 62 (6), 063301
- https://doi.org/10.1063/5.0023227
Abstract
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.This publication has 38 references indexed in Scilit:
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