Abstract
Consistency of the maximum-likelihood estimator (MLE) of a (multidimensional) parameter entering the drift term of an Itô equation is investigated. The results concern both ergodic and transient and even exploding solutions. The datum for the estimation is one sample-path (s-p). Accordingly, the definition of consistency is localised and the (sufficient) consistency condition is formulated in terms of a given s-p. In this way the consistency inference is based on the datum exclusively, and the convergence of the estimator can be analysed independently of whether the MLE is globally consistent (convergent for all possible data) or not. The theoretical considerations are illustrated by the numerical simulations of estimation of parameters of stochastic Duffing oscillator in ergodic, transient and exploding cases. Some essential computational aspects are clarified.
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© 1989 Springer-Verlag
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Kazimierczyk, P. (1989). Consistent ML estimator for drift parameters of both ergodic and nonergodic diffusions. In: Zabczyk, J. (eds) Stochastic Systems and Optimization. Lecture Notes in Control and Information Sciences, vol 136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0002692
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DOI: https://doi.org/10.1007/BFb0002692
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