LAN property for stochastic differential equations driven by fractional Brownian motion of Hurst parameter H∈(1/4,1/2)
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In this paper, we consider the problem of estimating the drift parameter of solution to the stochastic differential equation driven by a fractional Brownian motion with Hurst parameter less than 1/2 under complete observation. We derive a formula for the likelihood ratio and prove local asymptotic normality when H ∈ (1/4,1/2). Our result shows that the convergence rate is T^-1/2 for the parameters satisfying a certain equation and T^-(1-H) for the others.
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