Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of the underlying processes.

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Let X be a solution of a stochasti Let X be a solution of a stochastic integral equation driven by a fractional Brownian motion BH and let Vn(X, 2) = \sumn k=1(\DeltakX)2, where \DeltakX = X( k+1/n ) - X(k/n ). We study the ditions n2H-1Vn(X, 2) convergence almost surely as n → ∞ holds. This fact is used to obtain a strongly consistent estimator of the Hurst index H, 1/2 < H < 1.

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