Identification of a hereditary system with distributed delay
type: Item
instance of: scholarly article
title: Identification of a hereditary system with distributed delay
zbMATH Open document ID: 0568.93064
DOI: 10.1016/0167-6911(85)90032-5
author: Arunabha Bagchi
published in: Systems \& Control Letters
publication date: 1985-01-01T00:00:00Z
full work available at URL: identification-of-a-hereditary-system-with-distributed-delay(1f502714-558b-4625-af81-1e63e6fe8d9c).html
review text: The maximum likelihood method for identifying the parameter function in a linear hereditary system is considered. The delay is allowed to be distributed and so the classical theory is not directly applicable, since even if the maximum likelihood method is valid the estimates obtained may not be consistent. The system model is \[ dX_ t=\int^{0}_{-b}\alpha (\theta)X_{t+\theta}d\theta dt+dW_ t \] and \(\alpha\) is estimated by using finite-dimensional approximations in the space \(L^ 2[-b,0]\). This gives rise to the finite-dimensional maximum likelihood estimate \({\hat \alpha}{}^ T(\theta)\) for the process \(\{X_ t\), \(t_ 0\leq t\leq T\}\). Sufficient conditions are given for the consistency of the estimate, i.e. \[ \lim_{T\to \infty}\int^{T}_{t_ 0}| {\hat \alpha}^{(T)}(\theta)-\alpha (\theta)|^ 2d\theta =0, \] in probability.
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 3908303
zbMATH Keywords: maximum likelihood method
zbMATH Keywords: linear hereditary system
zbMATH Keywords: finite-dimensional approximations
zbMATH Keywords: consistency
reviewed by: S. P. Banks
MaRDI profile type: Publication
OpenAlex ID: W2146857007
cites work: Q3682311
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cites work: Identification of Nonstationary Diffusion Model by the Method of Sieves
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description: scientific article; zbMATH DE number 3908303