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This article is concerned with the drift parameter estimation for Ornstein–Uhlenbeck process driven by small  α -stable noises. The contrast function is given to obtain the least squares estimators and the error of estimation are obtained. The consistency, the rate of convergence and asymptotic distribution of estimators are derived when a small dispersion coefficientandsimultaneously. Some numerical calculus and simulations are made to verify the effectiveness of the estimators.

Least squares estimation for discretely observed Ornstein–Uhlenbeck process driven by small stable noises