On the specific nature of Hurst exponent esti-mates of the fractional Brownian motion

Sergey Porshnev, Eduard Solomaha

Abstract


A study of statistical characteristics of samples, ensembles of estimates of the Hurst exponents was conducted. The analysis of the obtained results showed that ensembles of estimates of the Hurst exponents are samples of random numbers with limited dispersion regions; the dependence is described by a step function. It turns out that it is possible to establish a one-to-one correspondence between the estimate calculated from a single implementation of the FBD and the "exact" value used to generate it only between the step number and the exact value changing with the step. To calculate estimates of the Hurst exponent of the FBD , the values of which will correspond to the "exact" value used to generate it, it is necessary to use an ensemble of independent implementations of the FBD , for each of which, a priori, there is reason to believe that the corresponding "exact" values of their Hurst exponents are the same

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