Didier, Gustavo; Zhang, Kui The asymptotic distribution of the pathwise mean squared displacement in single particle tracking experiments. (English) Zbl 1370.92039 J. Time Ser. Anal. 38, No. 3, 395-416 (2017). Summary: Microrheology is the study of the properties of biological complex fluids through the anomalous diffusion of small embedded particles. The main statistic for characterizing anomalous diffusion is the so-named mean squared displacement (MSD) of the particles. Notwithstanding the central statistical role of the MSD, its asymptotic distribution has not yet been established. In this paper, we assume that the particle motion is a Gaussian, stationary-increment stochastic process. We show that as the sample and the increment lag sizes go to infinity, the MSD displays Gaussian or non-Gaussian limiting distributions, as well as distinct convergence rates, depending on the diffusion exponent parameter. Cited in 2 ReviewsCited in 5 Documents MSC: 92C35 Physiological flow 62P10 Applications of statistics to biology and medical sciences; meta analysis 82B31 Stochastic methods applied to problems in equilibrium statistical mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 60G22 Fractional processes, including fractional Brownian motion Keywords:anomalous diffusion; viscoelastic fluid; mean squared displacement; fractional Brownian motion; fractional Ornstein-Uhlenbeck process; microrheology; Rosenblatt distribution PDFBibTeX XMLCite \textit{G. Didier} and \textit{K. Zhang}, J. Time Ser. 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