Undamped harmonic oscillator driven by additive Gaussian white noise: a statistical analysis

Abstract

While consistency of the maximum likelihood estimator of the drift matrix in a multi-dimensional continuous time Ornstein-Uhlenbeck pro- cess holds under rather general conditions, little is known about the rate of convergence and the limiting distribution of the estimator when the un- derlying process is not ergodic. The objective of the paper is to investigate these questions for an important example of a non-ergodic two-dimensional Ornstein-Uhlenbeck process: an undamped harmonic oscillator.