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The Asymptotic Distribution of The Pathwise Mean Squared Displacement in Single Particle Tracking Experiments
Author(s) -
Didier Gustavo,
Zhang Kui
Publication year - 2017
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12208
Subject(s) - mathematics , microrheology , gaussian , mean squared displacement , statistical physics , anomalous diffusion , diffusion , displacement (psychology) , gaussian process , convergence (economics) , exponent , mathematical analysis , physics , viscoelasticity , thermodynamics , economic growth , psychology , knowledge management , linguistics , philosophy , innovation diffusion , quantum mechanics , computer science , economics , psychotherapist , molecular dynamics
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.