Parameter estimation for the Langevin equation with stationary-increment Gaussian noise



We study the Langevin equation with stationary-increment Gaussian noise. We show the strong consistency and the asymptotic normality with Berry–Esseen bound of the so-called second moment estimator of the mean reversion parameter. The conditions and results are stated in terms of the variance function of the noise. We consider both the case of continuous and discrete observations. As examples we consider fractional and bifractional Ornstein–Uhlenbeck processes. Finally, we discuss the maximum likelihood and the least squares estimators.


Gaussian processes Langevin equation Ornstein–Uhlenbeck processes Parameter estimation 

Mathematics Subject Classification

60G15 62M09 62F12 


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of VaasaVaasaFinland
  2. 2.Department of Mathematics and System AnalysisAalto University School of Science, HelsinkiAaltoFinland

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