On the distribution of estimators of diffusion constants for Brownian motion

Details On the distribution of estimators of diffusion constants for Brownian motion On the distribution of estimators of diffusion constants for Brownian motion

2011-05-16

arxiv.org/abs/1105.3135v2

J. Phys. A: Math. Theor. 44 (2011) 335003

Physics

Condensed Matter

Statistical Mechanics

14 pages, 5 figures

Scientific paper

We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of quadratic functionals of Brownian motion that correspond to the Euclidean path integral for simple Harmonic oscillators with time dependent frequencies. Explicit analytical results are given for the distribution of the diffusion constant estimator in a number of cases and our results are confirmed by numerical simulations.

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