Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space-valued stochastic differential equations (Q759721)

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.