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

Tommi Sottinen*, Lauri Viitasaari

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)569–601
Number of pages33
JournalStatistical Inference for Stochastic Processes
Volume21
Issue number3
DOIs
Publication statusPublished - Oct 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Gaussian processes
  • Langevin equation
  • Ornstein–Uhlenbeck processes
  • Parameter estimation

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