PARAMETER ESTIMATION FOR AN ORNSTEIN-UHLENBECK PROCESS DRIVEN BY A GENERAL GAUSSIAN NOISE |
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作者姓名: | Yong CHEN Hongjuan ZHOU |
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作者单位: | School of Mathematics and Statistics;School of Mathematical and Statistical Sciences |
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基金项目: | supported by NSFC(11871079,11961033,11961034). |
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摘 要: | In this paper,we consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process(Gt)t≥0.The second order mixed partial derivative of the covariance function R(t,s)=EGtGs]can be decomposed into two parts,one of which coincides with that of fractional Brownian motion and the other of which is bounded by(ts)β-1up to a constant factor.This condition is valid for a class of continuous Gaussian processes that fails to be self-similar or to have stationary increments;some examples of this include the subfractional Brownian motion and the bi-fractional Brownian motion.Under this assumption,we study the parameter estimation for a drift parameter in the Ornstein-Uhlenbeck process driven by the Gaussian noise(Gt)t≥0.For the least squares estimator and the second moment estimator constructed from the continuous observations,we prove the strong consistency and the asympotic normality,and obtain the Berry-Esséen bounds.The proof is based on the inner product's representation of the Hilbert space(h)associated with the Gaussian noise(Gt)t≥0,and the estimation of the inner product based on the results of the Hilbert space associated with the fractional Brownian motion.
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关 键 词: | Fourth moment theorem Ornstein-Uhlenbeck process Gaussian process Malliavin calculus |
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