On the equivalence of two methods for interpolation
On the Kaczmarz algorithm of approximation in infinite-dimensional spaces
The Kaczmarz algorithm of successive projections suggests the following concept. A sequence of unit vectors in a Hilbert space is said to be effective if for each vector x in the space the sequence (xₙ) converges to x where (xₙ) is defined inductively: x₀ = 0 and , where . We prove the effectivity of some sequences in Hilbert spaces. We generalize the concept of effectivity to sequences of vectors in Banach spaces and we prove some results for this more general concept.
On the level crossing of multi-dimensional delayed renewal processes.
On the linear prediction problem of certain non-stationary stochastic processes.
On the rate of strong mixing in stationary Gaussian random fields
Rosenblatt showed that a stationary Gaussian random field is strongly mixing if it has a positive, continuous spectral density. In this article, spectral criteria are given for the rate of strong mixing in such a field.
On Vershik's standardness criterion and Tsirelson's notion of cosiness
One-Step Prediction for P...-Weakly Stationary Processes.
Optimising prediction error among completely monotone covariance sequences.
Outer factorization of operator valued weight functions on the torus
An exact criterion is derived for an operator valued weight function on the torus to have a factorization , where the operator valued Fourier coefficients of Φ vanish outside of the Helson-Lowdenslager halfplane , and Φ is “outer” in a related sense. The criterion is expressed in terms of a regularity condition on the weighted space of vector valued functions on the torus. A logarithmic integrability test is also provided. The factor Φ is explicitly constructed in terms of Toeplitz operators...
Prediction for Two Processes and the Nehari Problem.
Prediction of time series by statistical learning: general losses and fast rates
We establish rates of convergences in statistical learning for time series forecasting. Using the PAC-Bayesian approach, slow rates of convergence √ d/n for the Gibbs estimator under the absolute loss were given in a previous work [7], where n is the sample size and d the dimension of the set of predictors. Under the same weak dependence conditions, we extend this result to any convex Lipschitz loss function. We also identify a condition on the parameter space that ensures similar rates for the...
Prediction problems [Book]
Prédiction scalaire ou prédiction vectorielle pour des processus faiblement stationnaires
Prediction sequences in smooth Banach spaces
Quelques calculs de compensateurs impliquant l'injectivité de certains processus croissants
Questions de théorie des flots (I)
Questions de théorie des flots (VII)
Random measures and harmonizable sequences
Some problems arising from prediction theory and a theorem of Kolmogorov.
Some remarks on duality of stationary sequences
The paper clarifies the connection between Urbanik's and Miamee and Pourahmadi's concepts of duality for univariate weakly stationary random sequences. Some of Urbanik's results are proved in an alternative way and at the same time generalized to the multivariate case.