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Zbl 0768.62086
Kallianpur, G.; Selukar, R.S.
Parameter estimation in linear filtering.
(English)
[J] J. Multivariate Anal. 39, No.2, 284-304 (1991). ISSN 0047-259X

Let a partially observable random process $(x\sb t,y\sb t)$, $t\ge 0$, be given, where only the second component $(y\sb t)$ is observed. Suppose that $(x\sb t,y\sb t)$ satisfy the following system of stochastic differential equations driven by independent Wiener processes $(W\sb 1(t))$ and $(W\sb 2(t))$: $$dx\sb t=-\beta x\sb t dt+dW\sb 1(t),\ x\sb 0=0,\ dy\sb t=\alpha x\sb t dt+dW\sb 2(t),\ y\sb 0=0;\ \alpha,\beta\in(a,b),\ \alpha>0.$$ The local asymptotic normality of the model is proved and a large deviation inequality for the maximum likelihood estimator of the parameter $\theta=(\alpha,\beta)$ is obtained. This implies strong consistency, efficiency, asymptotic normality and the convergence of moments for the maximum likelihood estimator.
[M.P.Moklyachuk (Kiev)]
MSC 2000:
*62M20 Prediction, etc. (statistics)
62M09 Non-Markovian processes: estimation
62G05 Nonparametric estimation
62M99 Inference from stochastic processes
60F10 Large deviations

Keywords: linear filtering; Kalman filter; partially observable random process; independent Wiener processes; local asymptotic normality; large deviation inequality; maximum likelihood estimator; strong consistency; efficiency; asymptotic normality; convergence of moments

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