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Periodic observations of harmonizable symmetric stable sequences

Klotz L., Riedel M.

Probability and Mathematical Statistics

2005

Vol. 25, Fasc. 2

289--306

For harmonizable symmetric stable sequences we solve the following prediction problem: Assume that the values of the sequence are known at all odd integers. Compute the metric projection of an unknown value onto the space spanned by the known values as well as the corresponding approximation error. We study several questions related to this prediction problem such as regularity and singularity, Wold type decomposition, interrelations between the spaces spanned by the values at the even and odd integers, respectively.

Continuity of the metric projection in Orlicz space

Teng Y., Wang T., Li M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

[Z] 39

109-116

Let (f(n)) be a sequence of functions converging in norm to f in some rotund Orlicz function or se-quence space endowed with the Luxemburg norm or the Orlicz norm, and let (C(n)) be a sequence of convex sets satisfying some condition and tending in suitable way to a ser C. Then the best norm approximation of f(n) with respect to C(n) converges in norm to the best approximation of f with respect to C.