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Titlebook: Stochastic Systems: The Mathematics of Filtering and Identification and Applications; Proceedings of the N Michiel Hazewinkel,Jan C. Willem

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State Space Models for Gaussian Stochastic Processesequation-type representations are obtained. This paper is an abridged version of a forthcoming paper, which in turn summarizes and considerably extends results which have previously been presented in a series of preliminary conference papers.
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System Identificationthe true stochastic structure. In the third section the estimation of the order is discussed and a number of new results are presented. Other topics briefly considered are the construction of initial estimates for an iterative solution of the likelihood equations, time varying parameter models and non-linear models.
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Recursive Identificationion. Thus, asymptotically, no loss of information is encountered, despite the recursiveness of the method..Some user aspects and choices are also briefly discussed, and implications for adaptive control are commented upon.
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An Introduction to Nonlinear Filteringmalized conditional density. The filtering problem concerns the estimation of an unobserved stochastic process x. given observations of a related process y.; the classic problem is to calculate, for each t, the conditional distribution of x. given y., 0 ≤ s ≤ t. First, a brief review of key results
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Recursive Identificationrror methods” is chosen, within which many methods appear as special cases or as certain approximative variants..Special attention is paid to asymptotic convergence properties. The family of recursive prediction error methods is shown to converge to a local minimum of a certain criterion function. I
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Tests of Adequacy for Arma Models and Tests of Separated Hypothesesfication, recursive linear and non linear filtering and adaptive control. When we have identified a model we need to test its adequacy: it is this subject we want to discuss here. In a first part we are going to give some developments on the main tests used in the Arma case to verify the model. In a
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