BOYER, Denis; DEAN, David S.; MEJÍA-MONASTERIO, Carlos; OSHANIN, Gleb

doi:10.1140/epjst/e2013-01729-y

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BOYER, Denis
Instituto de Fisica

DEAN, David S.
Laboratoire Ondes et Matière d'Aquitaine [LOMA]

MEJÍA-MONASTERIO, Carlos
Laboratory of Physical Properties
Department of Mathematics and Statistics [Helsinki]

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The European Physical Journal. Special Topics. 2013, vol. 216, n° 1, p. 57-71

EDP Sciences

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Modern developments in microscopy and image processing are revolutionising areas of physics, chemistry, and biology as nanoscale objects can be tracked with unprecedented accuracy. However, the price paid for having a direct visualisation of a single particle trajectory with high temporal and spatial resolution is a consequent lack of statistics. This naturally calls for reliable analytical tools which will allow one to extract the properties specific to a statistical ensemble from just a single trajectory. In this article we briefly survey different analytical methods currently used to determine the ensemble average diffusion coefficient from single particle data and then focus specifically on weighted least-squares estimators, seeking the weight functions for which such estimators are ergodic. Finally, we address the question of the effects of disorder on such estimators.< Leer menos

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Optimal least-squares estimators of the diffusion constant from a single Brownian trajectory

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