Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space-valued stochastic differential equations
type: Item
instance of: scholarly article
title: Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space-valued stochastic differential equations
zbMATH Open document ID: 0553.93059
DOI: 10.1016/0304-4149(84)90004-8
author: Wilfried Loges
published in: Stochastic Processes and their Applications
publication date: 1984-01-01T00:00:00Z
review text: The author proves some Girsanov type theorems for Hilbert space valued Wiener processes and for linear stochastic evolution equations in Hilbert space, of the type \(dx=\theta Axdt+D(t)dw(t)\). He applies this to a parameter estimation problem for \(\theta\) with \(D(t)=I\) and obtains conditions for strong consistency and asymptotic normality of the maximum likelihood estimator.
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 46C99
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C25
zbMATH DE Number: 3882318
zbMATH Keywords: Girsanov type theorems
zbMATH Keywords: Hilbert space valued Wiener processes
zbMATH Keywords: linear stochastic evolution equations
zbMATH Keywords: parameter estimation
MaRDI profile type: Publication
full work available at URL: 0304-4149(84)90004-8
OpenAlex ID: W2033798227
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description: scientific article; zbMATH DE number 3882318