We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = (a0 - θ0Xt)dt + dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case (a0, θ0) = (0, 0). If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 > 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case (θ0 = 0) and for ergodic case (θ0 > 0) are completely different.
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