We study the problem of parameter estimation for generalized Ornstein-Uhlenbeck processes with small Lévy noises, observed at n regularly spaced time points on [0, 1]. Least squares method is used to obtain an estimator of the drift parameter. The consistency and the rate of convergence of the least squares estimator (LSE) are established when a small dispersion parameter [epsilon]-->0 and n-->[infinity] simultaneously. The asymptotic distribution of the LSE in our general setting is shown to be the convolution of a normal distribution and a stable distribution. The obtained results are different from the classical cases where asymptotic distributions are normal.
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Volume (Year): 79 (2009) Issue (Month): 19 (October) Pages: 2076-2085 Download reference. The following formats are available: HTML
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