# Parameter Estimation for an Ornstein-Uhlenbeck Process Driven by a General Gaussian Noise

@article{Chen2021ParameterEF, title={Parameter Estimation for an Ornstein-Uhlenbeck Process Driven by a General Gaussian Noise}, author={Yong Chen and Hongjuan Zhou}, journal={Acta Mathematica Scientia}, year={2021}, volume={41}, pages={573-595} }

In this paper, we consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process ( G t ) t ≥0 . The second order mixed partial derivative of the covariance function $$R(t,s) = \mathbb{E}\left[ {{G_t}{G_s}} \right]$$ 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 −1 up to a constant factor. This condition is valid for a class of continuous…

## 2 Citations

Berry-Esseen bounds and almost sure CLT for the quadratic variation of a general Gaussian process

- Mathematics
- 2021

Abstract. In this paper, we consider the explicit bound for the second-order approximation of the quadratic variation of a general fractional Gaussian process (Gt)t≥0. The second order mixed partial…

Parameter estimation for Vasicek model driven by a general Gaussian noise

- Mathematics, Computer ScienceCommunications in Statistics - Theory and Methods
- 2021

A least squares estimator and a moment estimator are constructed for the drift parameters of the Vasicek model and the consistency and the asymptotic normality are proved.

## References

SHOWING 1-10 OF 47 REFERENCES

Least squares estimator for non-ergodic Ornstein-Uhlenbeck processes driven by Gaussian processes

- Mathematics
- 2015

Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter

- Mathematics
- 2017

This paper studies the least squares estimator (LSE) for the drift parameter of an Ornstein–Uhlenbeck process driven by fractional Brownian motion, whose observations can be made either continuously…

Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case

- Mathematics
- 2011

We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a…

Berry-Esseen bounds and almost sure CLT for the quadratic variation of a general Gaussian process

- Mathematics
- 2021

Abstract. In this paper, we consider the explicit bound for the second-order approximation of the quadratic variation of a general fractional Gaussian process (Gt)t≥0. The second order mixed partial…

Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process

- Mathematics
- 2002

We consider the fractional analogue of the Ornstein–Uhlenbeck process, that is, the solution of a one-dimensional homogeneous linear stochastic differential equation driven by a fractional Brownian…

The Least Squares Estimator for an Ornstein-Uhlenbeck Process Driven by a Hermite Process with a Periodic Mean

- Mathematics
- 2021

We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes $$d{Y_s} = \left( {\sum\limits_{j = 1}^k {{\mu _j}{\phi _j}\left( s \right) - \beta {Y_s}} } \right){\rm{d}}s…

Parameter Estimation of Complex Fractional Ornstein-Uhlenbeck Processes with Fractional Noise

- Mathematics
- 2017

We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending…

Statistical Inference for Ergodic Diffusion Processes

- Mathematics
- 2006

Lévy Processes” (eight papers), “III. Empirical Processes” (four papers), and “IV. Stochastic Differential Equations” (four papers). Here are some comments about the individual papers: In I.2 (paper…

Least squares estimation for the drift parameters in the sub-fractional Vasicek processes

- MathematicsJournal of Statistical Planning and Inference
- 2018