Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space-valued stochastic differential equations (Q759721)
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scientific article; zbMATH DE number 3882318
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space-valued stochastic differential equations |
scientific article; zbMATH DE number 3882318 |
Statements
Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space-valued stochastic differential equations (English)
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1984
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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.
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Girsanov type theorems
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Hilbert space valued Wiener processes
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linear stochastic evolution equations
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parameter estimation
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