LAN property for stochastic differential equations with additive fractional noise and continuous time observation

Yanghui Liu, Eulalia Nualart and Samy Tindel

Stochastic Processes and their Applications, 2019, vol. 129, issue 8, 2880-2902

Abstract: We consider a stochastic differential equation with additive fractional noise with Hurst parameter H>1∕2, and a non-linear drift depending on an unknown parameter. We show the Local Asymptotic Normality property (LAN) of this parametric model with rate τ as τ→∞, when the solution is observed continuously on the time interval [0,τ]. 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.

Keywords: Fractional Brownian motion; Parameter estimation; Ergodicity (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2018.08.008

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