This paper reviews some fundamental results in prediction theory, spectral factorization and
Wiener filtering with a particular focus on questions of computability. Since the mathematical …

This paper investigates the complexity of computing the minimum mean square prediction
error for wide-sense stationary stochastic processes. It is shown that if the spectral density of …

This paper gives a complete characterization of the complexity of computing the minimum
mean square pre-diction error for wide-sense stationary stochastic processes. It shows that if …

The most obvious points of contact between linear and matrix algebra and statistics are in
the area of multivariate analysis. We review the way that, as both developed during the last …

In this paper we show that the empirical eigenvalue distribution of any sample covariance
matrix generated by independent samples of a stationary regular sequence has a limiting …

We characterize even measures μ= wd x+ μ s on the real line R with finite entropy integral∫
R log⁡ w (t) 1+ t 2 dt>−∞ in terms of 2× 2 Hamiltonians generated by μ in the sense of the …

In this paper, it will be shown that the minimum mean square error (MMSE) for predicting a
stationary stochas-tic time series from its past observations is not generally Turing …

The paper considers causal smoothing of the real sequences, ie, discrete time processes in
a deterministic setting. A family of causal linear time-invariant filters is suggested. These …

This paper deals with geometry of covariance matrices to define new advanced Radar
Doppler Processing based on Metric Space tools. Information Geometry has been …

We proposed in this work the introduction of a new vision of stochastic processes through
geometry induced by dilation. The dilation matrices of a given process are obtained by a …