In this paper we show how the zero dynamics of (not necessarily square) spectral factors relate to the splitting subspace geometry of stationary stochastic models and to the corresponding algebraic… (More)

In this paper we show that for linear switching systems of the form xn+1 = Anxn + un+1, where the matrices An are chosen arbitrarily from a given set of matrices, bounded-input-bounded-output… (More)

The estimation of Hidden Markov Models (HMMs) has attracted a lot of attention recently, see results of [29], [30]. The purpose of this paper is to lay the foundation of a new approach for the… (More)

In this paper we analyze the structure of the class of discrete-time linear stochastic systems in terms of the geometric theory of stochastic realization. We discuss the role of invariant directions,… (More)

Rudas, Clogg, and Lindsay (1994, J. R Stat Soc. Ser. B, 56, 623) introduced the so-called mixture index of fit, also known as pi-star (π*), for quantifying the goodness of fit of a model. It is the… (More)

We consider hidden Markov processes in discrete time with a finite state space X and a general observation or read-out space Y , which is assumed to be a Polish space. It is well-known that in the… (More)

The weak convergence of a sample sum, in a generalized rejective sampling from a finite population, to a Poisson and Normal distribution is discussed. The generalization consists in assuming that the… (More)

We investigate here the interpolation conditions connected to an interpolating functionQ obtained as a Linear Fractional Transformation of another function S. In general, the degree ofQ is equal to… (More)

We consider finite state continuous read-out hidden Markov models. The exponential stability of the predictive filter was investigated by LeGland and Mevel (2000) when the transition probability… (More)