On the distribution of estimators of diffusion constants for Brownian motion

被引：16

作者：

Boyer, Denis ^{[1
,2
]}

Dean, David S. ^{[2
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Fis, Mexico City 04510, DF, Mexico

[2] Univ Toulouse, Theoret Phys Lab, IRSAMC, CNRS, F-31062 Toulouse, France

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2011年 / 44卷 / 33期

关键词：

SINGLE-PARTICLE TRACKING; FUNCTIONALS;

D O I：

10.1088/1751-8113/44/33/335003

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页数：13

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