Abstract
The aim of this paper is to bridge the gap between the mathematical theory of maximum likelihood estimation (MLE) for Itô equations and the practice of identification of engineering systems. A systematic extension of the theory is outlined to enable the ML parametric identification of systems which are not necessarily Markovian, ergodic and stationary, and which may explode in finite time. Accuracy of estimation (consistency) and robustness problems are also investigated. The discussion is illustrated by the analysis of a number of examples, connected with fundamental models of stochastic fracture mechanics and with random vibration.
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