We investigate random
sequences $(X_n)_{\nin_0}$ with spectral representation
based on certain orthogonal polynomials, that is, random
sequences that are weakly stationary with respect to
polynomial hypergroups. We present various situations where
one meets this kind of sequence. The main topic is on the
one-step prediction. In particular, it is examined when the
mean-squared error tends to zero. For many cases we present
a complete solution for the problem of $(X_n)_{\nin_0}$
being asymptotically deterministic.
Publié le : 2003-01-14
Classification:
Prediction,
random sequences,
orthogonal polynomials,
hypergroups,
60G10,
60G25,
43A62
@article{1046294305,
author = {H\"osel, Volker and Lasser, Rupert},
title = {Prediction of weakly stationary sequences on polynomial hypergroups},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 93-114},
language = {en},
url = {http://dml.mathdoc.fr/item/1046294305}
}
Hösel, Volker; Lasser, Rupert. Prediction of weakly stationary sequences on polynomial hypergroups. Ann. Probab., Tome 31 (2003) no. 1, pp. 93-114. http://gdmltest.u-ga.fr/item/1046294305/