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Minimum contrast estimator for fractional Ornstein-Uhlenbeck processes. (English) Zbl 1274.62567

Summary: This paper proposes a minimum contrast methodology to estimate the drift parameter for the Ornstein-Uhlenbeck process driven by fractional Brownian motion of Hurst index, which is greater than one half. Both the strong consistency and the asymptotic normality of this minimum contrast estimator are studied based on the Laplace transform. The numerical simulation results confirm the theoretical analysis and show that the minimum contrast technique is effective and efficient.

MSC:

62M09 Non-Markovian processes: estimation
60G22 Fractional processes, including fractional Brownian motion
60H07 Stochastic calculus of variations and the Malliavin calculus
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

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