Abstract
The paper studies long time asymptotic properties of the Maximum Likelihood Estimator (MLE) for the signal drift parameter in a partially observed fractional diffusion system. Using the method of weak convergence of likelihoods due to Ibragimov and Khasminskii (Statistics of random processes, 1981), consistency, asymptotic normality and convergence of the moments are established for MLE. The proof is based on Laplace transform computations.
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Brouste, A., Kleptsyna, M. Asymptotic properties of MLE for partially observed fractional diffusion system. Stat Inference Stoch Process 13, 1–13 (2010). https://doi.org/10.1007/s11203-009-9035-x
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DOI: https://doi.org/10.1007/s11203-009-9035-x