Smoothing and likelihood ratio for Gaussian boundary value processes

A new derivation, which does not need the invertibility assumption of the covariance matrix of the boundary data, is given for the smoothing of Gaussian two-point boundary value processes (TPBVP). The likelihood ratio for TPBV processes is then derived in terms of the system parameters by using the Krein factorization. The likelihood ratio involves the smoother of the process. An alternate expression for the likelihood ratio based on the filtered estimate of the state is also given.<
>