科研之友
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摘要
We show that thinning of increments of the fractional Brownian motion with Hurst exponent H not equal 1/2 breaks its H-self-similarity property. As a result, we obtain a new Gaussian process with stationary increments which is not the fractional Brownian motion for any H. Moreover, in the subdiffusion case (H < 1/2), the new process statistically resembles the classical Brownian motion (H = 1/2). To this end, we study analytically the second moment of such processes. Finally, Monte Carlo simulations show that the H estimator obtained by mean square displacement is close to the Brownian motion case with H = 1/2. These results show that stationary data describing anomalous diffusion phenomenon can lead to different statistical conclusions for different resolution of measurement. Therefore, one should be very careful in statistical inference, especially in strong subdiffusion regimes (H approximate to 0).
- 出版日期2012-5
