Properties and distribution of the dynamical functional for the fractional Gaussian noise

摘要

The fractional Brownian motion and its increment process, the fractional Gaussian noise (fGn), are highly popular models for data exhibiting anomalous diffusion. In this paper, an explicit formula for the dynamical functional, a tool for testing ε-ergodicity breaking and a statistic helpful in the process identification, is provided for the fractional Gaussian noise. Its basic characteristics are derived and the distribution of its single trajectory estimator is studied. Additionally, the sensibility of the convergence of the dynamical functional to the Hurst parameter H is analysed.