Parameter Estimation for an Ornstein-Uhlenbeck Process Driven by a General Gaussian Noise
Parameter Estimation for an Ornstein-Uhlenbeck Process Driven by a General Gaussian Noise
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DOI：
10.1007/s10473-021-0218-x
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发表时间：
2020-02
影响因子：
1
通讯作者：
Yong Chen;Hongjuan Zhou
中科院分区：
文献类型：
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作者：
Yong Chen;Hongjuan Zhou
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 functioncan 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 spaceassociated 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.
