Maximum likelihood estimation for reflected Ornstein-Uhlenbeck processes with jumps

ABSTRACT

In this paper, we investigate the maximum likelihood estimation for the reflected Ornstein-Uhlenbeck processes with jumps based on continuous observations. We derive likelihood functions by using semimartingale theory. From this we get explicit formulas for estimators. The strong consistence and asymptotic normality of estimators are proved by using the method of stochastic integration.

Keywords:

• Lévy process
• Maximum likelihood estimation
• Reflected Ornstein-Uhlenbeck process

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M05
• 62F10

Acknowledgements

The authors are also grateful to the anonymous referee for their helpful comments to improve this paper.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China(Grant No.11401029) and the National Natural Science Foundation of China(Grant No.11671104).