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Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises

Hongwei Long

Statistics & Probability Letters, 2009, vol. 79, issue 19, 2076-2085

Abstract: 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.

Date: 2009
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