Parameter identifiability with kullback-leibler information divergence criterion

We study the problem of parameter identifiability with Kullback-Leibler information divergence (KLID) criterion. The KLID-identifiability is defined, which can be related to many other concepts of identifiability, such as the identifiability with Fisher's information matrix criterion, identifiability with least-squares criterion, and identifiability with spectral density criterion. We also establish a simple check criterion for the Gaussian process and derive an upper bound for the minimal identifiable horizon of Markov process. Furthermore, we define the asymptotic KLID-identifiability and prove that, under certain constraints, the KLID-identifiability will be a sufficient or necessary condition for the asymptotic KLID-identifiability. The consistency problems of several parameter estimation methods are also discussed.