## Parameter estimation for fractional Ornstein-Uhlenbeck processes at discrete observation.(English)Zbl 1225.62116

Summary: This paper deals with the problem of estimating the parameters for fractional Ornstein-Uhlenbeck processes from discrete observations when the Hurst parameter $$H$$ is known. Both the drift and the diffusion coefficient estimators of discrete form are obtained based on approximating integrals via Riemann sums with Hurst parameter $$H \in (1/2, 3/4)$$. By adapting the stochastic integral representation to the fractional Brownian motion, these two estimators can be efficiently computed. Numerical examples are presented to examine the performance of our method. An application to real data is also presented to show how to apply this method in practice.

### MSC:

 62M05 Markov processes: estimation; hidden Markov models 60G22 Fractional processes, including fractional Brownian motion 60J60 Diffusion processes 65C50 Other computational problems in probability (MSC2010)

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