Title: Parameter estimation for partially observed linear stochastic system

Authors: Chao Wei

Addresses: School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China

Abstract: This paper is concerned with the problem of parameter estimation for a partially observed linear stochastic system. The state estimator is obtained by using the continuous-time Kalman linear filtering theory. The likelihood function is given based on the innovation theorem and Girsanov theorem, the parameter estimator and error of estimation are derived. The strong consistency of the parameter estimator and the asymptotic normality of the error of estimation are proved by applying ergodic theorem, maximal inequality for martingale, Borel-Cantelli lemma and the central limit theorem for stochastic integrals.

Keywords: linear stochastic system; parameter estimation; state estimation; strong consistency; asymptotic normality; incomplete observation; operational research; Kalman linear filtering; error of estimation; likelihood function.

DOI: 10.1504/IJMOR.2019.100741

International Journal of Mathematics in Operational Research, 2019 Vol.14 No.4, pp.590 - 599

Received: 22 Aug 2017
Accepted: 29 Dec 2017
Published online: 17 Jul 2019 *

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