LAN property for stochastic differential equations with additive fractional noise and continuous time observation |
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Authors: | Yanghui Liu Eulalia Nualart Samy Tindel |
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Institution: | 1. Department of Mathematics, Purdue University, 150 N. University Street, W. Lafayette, IN 47907, USA;2. Department of Economics and Business, Universitat Pompeu Fabra and Barcelona Graduate School of Economics, Ramón Trias Fargas 25-27, 08005 Barcelona, Spain |
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Abstract: | We consider a stochastic differential equation with additive fractional noise with Hurst parameter , and a non-linear drift depending on an unknown parameter. We show the Local Asymptotic Normality property (LAN) of this parametric model with rate as , when the solution is observed continuously on the time interval . The proof uses ergodic properties of the equation and a Girsanov-type transform. We analyze the particular case of the fractional Ornstein–Uhlenbeck process and show that the Maximum Likelihood Estimator is asymptotically efficient in the sense of the Minimax Theorem. |
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Keywords: | Corresponding author 62M09 62F12 Fractional Brownian motion Parameter estimation Ergodicity |
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