Asymptotic theory for the detection of mixing in anomalous diffusion
Probability
2021-06-16 v3 Statistical Mechanics
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.
Keywords
Cite
@article{arxiv.2007.14538,
title = {Asymptotic theory for the detection of mixing in anomalous diffusion},
author = {Kui Zhang and Gustavo Didier},
journal= {arXiv preprint arXiv:2007.14538},
year = {2021}
}