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

Ning Lin | Zendy; Sergey V. Lototsky | Zendy

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

Author(s) -

Ning Lin,

Sergey V. Lototsky

Publication year - 2011

Publication title -

communications on stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.224

H-Index - 10

eISSN - 2688-6669

pISSN - 0973-9599

DOI - 10.31390/cosa.5.1.13

Subject(s) - white noise , additive white gaussian noise , white (mutation) , gaussian noise , gaussian , noise (video) , harmonic analysis , acoustics , physics , statistical physics , mathematics , statistics , computer science , mathematical analysis , algorithm , quantum mechanics , artificial intelligence , image (mathematics) , biochemistry , chemistry , gene

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.

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