Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space-valued stochastic differential equations
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.
scientific article; zbMATH DE number 3882318