Maximum likelihood parameter estimation from incomplete data via the sensitivity equations: the continuous-time case

The problem of estimating the parameters for continuous-time partially observed systems is discussed. New exact filters for obtaining maximum likelihood (ML) parameter estimates via the expectation maximization algorithm are derived. The methodology exploits relations between incomplete and complete data likelihood and gradient of likelihood functions, which are derived using Girsanov's measure transformations. The ML parameter estimates are described by a set of Lyapunov sensitivity equations.