Maximum likelihood estimation in linear infinite dimensional models

Abstract

Consider a martingale with values in the strong dual of a nuclear space . Let c(t) satisfy the functional equation in which valued Gaussian white noise process and with , are continuous linear operators. It is shown that under suitable assumptions the initial condition c(0) can be chosen in such a way that becomes an ergodic stationary Markov process and the unknown parameter θcan be estimated by the maximum likelihood method. The obtained estimator of θis strongly consistent and satisfies a version of the central limit theorem