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A note on “Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises”. (English) Zbl 1203.62141

Summary: The asymptotic estimation of drift parameter is studied for generalized Ornstein-Uhlenbeck processes with small Lévy noises. We extend the work of H. Long [ibid. 79, No. 19, 2076–2085 (2009; Zbl 1171.62046)] and show that the main results of Long hold under the weaker conditions.

MSC:

62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators

Citations:

Zbl 1171.62046
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References:

[1] Barndorff-Nielsen, O. E.; Shephard, N., Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial econometrics, Journal of the Royal Statistical Society, Series B, 63, 167-241 (2001) · Zbl 0983.60028
[2] Billingsley, P., Convergence of Probability Measures (1999), John Wiley and Sons, Inc.: John Wiley and Sons, Inc. New York · Zbl 0172.21201
[3] Ethier, S. N.; Kurtz, T. G., Markov Processes: Characterization and Convergence (1986), John Wiley and Sons Inc.: John Wiley and Sons Inc. New York · Zbl 0592.60049
[4] Gloter, A.; Sørensen, M., Estimation for stochastic differential equations with a small diffusion coefficient, Stochastic Process. Appl., 119, 679-699 (2009) · Zbl 1157.62055
[5] Long, H., Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises, Statistics and Probability Letters, 79, 2076-2085 (2009) · Zbl 1171.62046
[6] Samorodnitsky, G.; Taqqu, M., Stable Non-Gaussian Random Processes (1994), Chapman and Hall: Chapman and Hall New York · Zbl 0925.60027
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