分数阶布朗运动广义扩散系数的遍历最小二乘估计
On ergodic least-squares estimators of the generalized diffusion coefficient for fractional Brownian motion
摘要：
基于单时间平方位移的加权泛函，研究了分数阶布朗运动$B_t$的广义扩散系数在Hurst指数$H$已知时的估计.我们表明，对于一定的选择的权重函数，这些泛函具有遍历性，从而提供了真正的，整体平均，广义扩散系数从一个单一的轨迹数据的任何必要的精度，但在一个逐步更高的实验分辨率为代价。在$H\simeq0.30$附近收敛最快，这是亚扩散区的一个值。
英文摘要：
We analyse a class of estimators of the generalized diffusion coefficient for fractional Brownian motion $B_t$ of known Hurst index $H$, based on weighted functionals of the single time square displacement. We show that for a certain choice of the weight function these functionals possess an ergodic property and thus provide the true, ensemble-averaged, generalized diffusion coefficient to any necessary precision from a single trajectory data, but at expense of a progressively higher experimental resolution. Convergence is fastest around $H\simeq0.30$, a value in the subdiffusive regime.
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