Berry-Esséen bound for drift estimation of fractional Ornstein Uhlenbeck process of second kind
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In the present paper we consider the Ornstein-Uhlenbeck process of the second kind defined as solution to the equation dX_t = -α X_tdt+dY_t^(1), X_0=0, where Y_t^(1):=∫_0^te^-sdB^H_a_s with a_t=He^t/H, and B^H is a fractional Brownian motion with Hurst parameter H∈(1/2,1), whereas α>0 is unknown parameter to be estimated. We obtain the upper bound O(1/√(T)) in Kolmogorov distance for normal approximation of the least squares estimator of the drift parameter α on the basis of the continuous observation {X_t,t∈[0,T]}, as T→∞. Our method is based on the work of <cit.>, which is proved using a combination of Malliavin calculus and Stein's method for normal approximation.
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