Parameter Estimation for Controlled Semilinear Stochastic Systems: Identifiability and Consistency

We consider a controlled stochastic semilinear evolution equation with the drift depending on the unknown parameter. We show that the maximum likelihood estimator is strongly consistent for a class of bounded predictable controls.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of multivariate analysis 2002-02, Vol.80 (2), p.322-343
Hauptverfasser:	Goldys, B., Maslowski, B.
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology identifiability infinitesimal generator invariant measure Mathematics maximum likelihood estimator Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use semilinear stochastic evolution equation semilinear stochastic evolution equation maximum likelihood estimator identifiability invariant measure strong law of large numbers transition semigroup infinitesimal generator Stochastic analysis strong law of large numbers transition semigroup
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Beschreibung
Zusammenfassung:	We consider a controlled stochastic semilinear evolution equation with the drift depending on the unknown parameter. We show that the maximum likelihood estimator is strongly consistent for a class of bounded predictable controls.
ISSN:	0047-259X 1095-7243
DOI:	10.1006/jmva.2001.1989