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We study some estimators of the Hurst index and the diffusion coefficient ofthe fractional Gompertz diffusion process and prove that they are stronglyconsistent and most of them are asymptotically normal. Moreover, we compare theasymptotic behavior of these estimators with the aid of computer simulations.

On comparison of the estimators of the Hurst index and the diffusion coefficient of the fractional Gompertz diffusion process