Hidden ergodic Ornstein–Uhlenbeck process and adaptive filter

Yury A. Kutoyants ()
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Yury A. Kutoyants: Le Mans University

Statistical Inference for Stochastic Processes, 2025, vol. 28, issue 1, No 4, 39 pages

Abstract: Abstract This paper revisits the state and parameter estimation problems for a system of partially observed linear stochastic differential equations. An asymptotically optimal adaptive filter of the hidden state process is constructed using a three stage procedure. First, the unknown parameter is estimated by means of the method of moments. Then this preliminary estimator is used to define the One-step MLE process by applying the scoring technique, and, finally, the improved estimator is plugged into Kalman-Bucy filter. The obtained parameter estimator and the adaptive filter are proved to be asymptotically efficient in the long-time regime.

Keywords: Partially observed linear system; Hidden Markov process; Kalman-Bucy filter; One-step MLE-process; On-line approximation; Adaptive filter (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11203-024-09321-6

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