Abstract
This paper presents a sequential estimator for some unknown parameters in stochastic linear systems with memory. As examples stochastic differential equations with time delayed drift are considered. Based on the maximum likelihood method, we construct an estimation procedure with given accuracy in the sense of the L p -norm (p≥ 2). It is shown, that this procedure works also in certain cases, when the normalized information matrix of the observed process is asymptotically degenerated. The almost surely consistency of the proposed estimators and the asymptotic behavior of the length of observations are derived.
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Küchler, U., Vasiliev, V. Sequential Identification of Linear Dynamic Systems with Memory. Statistical Inference for Stochastic Processes 8, 1–24 (2005). https://doi.org/10.1023/B:SISP.0000049119.79817.ee
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DOI: https://doi.org/10.1023/B:SISP.0000049119.79817.ee